Shafkat A. Beg

A Review on the Mathematical Modeling of Biofilm Processes: Advances in Fundamentals of Biofilm Modeling

An attempt is made to review the developments in the modeling of biofilm processes that have been made during the last fifteen years. This article considers only a selection of those publications that have created a significant impact on the trends and techniques of biofilm modeling. The recent advances in the areas of microbial interactions (multispecies biofilms) as well as the inclusion of ionic interactions and the pH effects in the biofilm modeling are also summarized.

Generalized kinematic viscosity—temperature correlation for undefined petroleum fractions

Abstract A generalized kinematic viscosity—temperature correlation for undefined liquid petroleum fractions has been developed to represent the data for a wid 200 and 850 °F. The only characterization properties required for estimation are the API gravity and 50% boiling point. Detailed analysis shows that

Effects of inhibitors on nitrification in a packed-bed biological flow reactor

The individual effect of trivalent arsenic, hexavalent chromium and fluoride on nitrification is studied under continuous load in a packed bed biological flow reactor. The results show that Michaelis-Menten rate expression gives the best representation of nitrification data in the absence of inhibitors. However, in the presence of inhibitors, the system follows a non-competitive mode of inhibition with the following rate expression: αi=VmaxSKS+SKiSKi+I. The values of Vmax and Ks are estimated as 1.466 mg l−1 min−1 and 2.349 mg l−1 respectively. The inhibitor constant Ki is evaluated as 273 mg l−1 for trivalent arsenic, 56 mg l−1 for hexavalent chromium and 1185 mg l−1 for fluoride.

Theoretical Analysis of a Packed-bed Biological Reactor for Various Reaction Kinetics

Abstract The performance characteristics of a packed-bed biological reactor have been analysed taking into consideration the diffusional resistance of the biofilm. The model equations are solved by the method of orthogonal collocation from the transient to the steady state condition for various reaction kinetics of practical significance, namely Michaelis-Menten kinetics with and without substrate inhibition. The effect of various process variables of physical importance are investigated parametrically. It is found that the substrate conversion increases with increase in the Peclet number, the mass transfer coefficient, the surface area of biofilm and the film thickness. However, the substrate conversion is not affected by the film thickness after it has exceeded a certain value. Furthermore, analyses for individual kinetics corresponding to the three classic modes of non-competitive, competitive and anti-competitive inhibition have been presented. The results show that inhibitor concentration decreases the substrate conversion and that the extent of the effect is a maximum for the non- competitive case and a minimum for the anti-competitive case.

Modeling of Axial and Recycle Backmixing Effects in a Biological Packed Bed Loop Reactor

Abstract A theoretical model for a packed bed biological loop reactor is presented by considering both external and internal resistances for the general case of Monod kinetics. Numerical solutions have been obtained by the method of orthogonal collocation for a wide range of saturation parameters to cover the two limiting cases of zero-order and first-order kinetics. The numerical solutions for the limiting cases were found to show good agreement with the analytical solutions. The effects of recycle ratio and axial dispersion on the performance of the reactor were studied parametrically. The results show that for low recycle ratios the conversion increases with decrease in Peclet number for first-order and Monod type kinetics; for zero-order kinetics, however, the conversion is independent of both Peclet number and recycle ratio. The effectiveness factor profiles along the length of the reactor were compared for Monod kinetics. It was found that an increase in recycle ratio tends to flatten the profile. The effect of axial dispersion on the concentration profiles at higher recycle ratio was found to be negligible. The dynamics of how steady state conditions are achieved in the reactor is also presented.

Chromium(VI) inhibition in multi-substrate carbon oxidation and nitrification process in an upflow packed bed biofilm reactor

Abstract The performance of an upflow packed bed biofilm reactor has been analyzed mathematically under multi-substrate limitation of carbon oxidation and nitrification reactions while subjected to inhibition of a continuous dose of Cr(VI). For a fixed inlet concentration of 150 mg l−1 of NH4+-N and 250 mg l−1 of acetate and varying the inlet concentrations of Cr(VI), the results show that the toxicity of Cr(VI) to both organic oxidation and nitrification processes increases rapidly with increase in its inlet concentration. The toxicity of Cr(VI) has been found to be much pronounced when nitrification alone is considered to take place in the reactor. The concentration profiles within the biofilm show that oxygen is a limiting component near the inlet and at the middle of the reactor. This necessitates the need for ample supply of oxygen at these locations within the reactor as major portion of oxidation of both acetate and NH4+-N takes place there. The model predictions show a close agreement with the available experimental data for a variety of operating conditions.

Analysis of non-isothermal tubular reactor packed with immobilized enzyme systems

Abstract The dynamic and steady state performance of a non-isothermal tubular reactor packed with spherical encapsulated enzyme particles has been modeled in terms of different dimensionless transport and kinetic parameters. The dynamic concentration profile for an initially substrate-free reactor reaches a maximum before achieving steady state. The steady state dimensionless bulk substrate concentration, unlike the temperature, progressively decreases along the reactor bed. On increase in the external mass transfer coefficient K L and Biot number Bi m for mass transfer, the concentration profile decreases more steeply. The simulation study shows that the biocatalyst particles may be considered isothermal. The exit substrate concentration decreases with increase in Peclet number Pe m for mass transfer, i.e. backmixing effects, indicating that a plug flow reactor will have a higher overall conversion than a perfect mixer. The dynamic bulk temperature rises more rapidly near the reactor inlet with increase in the Peclet number Pe h for heat transfer, i.e. thermal backmixing effects. The external resistance to mass and heat transfer becomes negligible above a critical value of K L and external heat transfer coefficient h . The bulk substrate concentration, unlike the temperature, decreases with increase in the dimensionless heat α of reaction. For typical Michaelis-Menten kinetics, the exit conversion and temperature will be limited between those for zero- and first-order kinetics.

Densities and excess volumes of the benzene-cyclohexane system between 298.15 and 473.15 k

Abstract Beg, S.A., Tukur, N.M., Al-Harbi, D.K. and Hamad, E., 1994. Densities and excess volumes of the benzene-cyclohexane system between 298.15 and 473.15 K. Fluid Phase Equilibria, 94: 289-300. This paper reports the results of measurements of the densities of binary mixtures of benzene with cyclohexane using a high pressure stainless steel pycnometer system for the whole composition range at various temperatures between 298.15 and 473.15 K. The experimental densities were compared with those predicted by the Hankison-Brobst-Thomson (HBT) correlation and the Spencer and Danner Modified Rackett (SDR) equation. Both the HBT and the SDR showed an average deviation of about 0.58%. The excess molar volumes, VE, calculated from the density values have been found to be positive for all the concentrations and temperatures considered.

Modelling of simultaneous methanogenesis and denitrification in an upflow packed-bed biofilm reactor

The performance of an upflow packed-bed biofilm reactor was investigated by considering simultaneous methanogenesis and denitrification reactions under step and sinusoidal variations of feed concentration and temperature. For simultaneous step inputs of 20 mg dm -3 of NO 3 - -N and 60 mg dm -3 of methanol, the proposed model shows that major conversion of both the substrates takes place in the first half of the reactor. However, when the inlet concentration of methanol is subjected to sinusoidal variation, while that of NO 3 - -N is maintained stepwise, the exit concentration of both methanol and NOj 3 - -N follow a sinusoidal response. On the other hand, when the inputs are reversed (methanol stepwise and NO 3 - -N sinusoidal), the response exhibits similar behaviour. For sinusoidal variation of feed temperature the exit concentration profiles of both substrates also follow a sinusoidal pattern. For methanol, the mean steady state conversion under sinusoidal variation is higher than the corresponding steady state concentration when feed temperature is constant at 30°C. The model predictions are in good agreement with the experimental data available in the literature.

Effects of enzyme microcapsule shape on the performance of a nonisothermal packed-bed tubular reactor

The effects of enzyme microcapsule shape (spherical, cylindrical and flat plate) on the performance of a nonisothermal, packed-bed reactor have been modeled as a function of Biot number and Peclet number for mass and heat transfer (Bi m , Bi h , Pe m and Pe h ), and dimensionless heat of reaction α. Under the given simulation conditions, only higher values of Bi m and Bi h (>2.5) confirm the influence of microcapsule shape on the reactor performance such that the axial and overall conversion and bulk temperature decrease as follows : spherical > cylindrical > flat plate. In terms of the shape-independent modified Biot number, Bi* = Bi/{(n + 1)/3), this order is retained for 2 < Bi* < 8. The influence of increasing Pe m , Pe h , and α on conversion and bulk temperature also follows the above order. For the flat plate, the exit conversion and temperature are not influenced by Pe m and Pe h , that is, mass transfer and thermal backmixing effects, respectively. On the other hand, for the spherical and cylindrical microcapsules, overall backmixing effects are negligible only beyond a critical value of Pe m (∼7) and Pe h (∼1.75). The conversion and bulk temperature increase with the increase in α, independent of the microcapsule shape. The spherical and cylindrical microcapsules, unlike the flat plate, cannot be considered isothermal.