Horacio A. Irazoqui

The radiation field for the point and line source approximations and the three-dimensional source models: Applications to photoreactions

Abstract A new and rigorous analysis of the properties of the radiation field as applied to photochemical reaction engineering is presented. The absorption constitutive equation as well as the steady state radiation balances are discussed both physically and mathematically. It is shown that any property related to the specific intensity will have a different definition and/or formulation depending upon the type of radiation source model used (a point, a line or one with all the spatial dimensions). The final objective is to obtain, for different types of radiation source models, equations for predicting flux density profiles as well as initiation rates inside photochemical reactors.

Selective Photocatalytic Oxidation of 4-Methoxybenzyl Alcohol to p-Anisaldehyde in Organic-Free Water in a Continuous Annular Fixed Bed Reactor

Photocatalytic oxidation of 4-methoxybenzyl alcohol to p-anisaldehyde was performed in water organic-free solutions by using a fixed bed continuous photoreactor containing Pyrex beads on which a TiO2 home prepared photocatalyst was supported. The influence of liquid flow rate, inlet alcohol concentration and catalyst amount on the photoprocess was studied. The highest selectivity to p-anisaldehyde was about 47% being CO2, the other main oxidation product; traces of 4-methoxybenzoic acid were also detected. The radiation field inside the photoreactor has been modelled by applying the Monte Carlo method thus allowing the determination of the local volumetric rate of photon absorption (LVRPA). It was found that the radiation intensity profile sharply decreases inside the bed so that an important aliquot of the bed is not active for the photoreaction occurrence. This finding indicates that the reactivity results, obtained by measuring the concentration values of reagents and products at the exit of photoreactor, can not be used jointly with the radiation modelling ones for determining the dependence of reaction kinetics on light intensity. The Langmuir-Hinshelwood approach has been satisfactorily applied for modelling the photoreactivity results and the values of all the model parameters have been determined.

The local and observed photochemical reaction rates revisited

In a broad sense, photochemical reactions proceed through pathways involving several reaction steps. The initiation step is the absorption of energy both by the reactant or sensitizer molecules and in some cases, by the catalyst, leading to intermediate products that ultimately give rise to stable end products. Preferably, the reaction rate expression is derived from a proposed mechanism together with sound simplifying assumptions; otherwise, it may be adopted on an empirical basis. Under a kinetic control regime, the rate expression thus obtained depends on the local rate of photon absorption according to a power law whose exponent very often ranges from one half to unity. The kinetic expression should be valid at every point of the reactor volume. However, due to radiation attenuation in an absorbing and/or scattering medium, the value of the photon absorption rate is always a function of the spatial position. Therefore, the overall photochemical reaction rate will not be uniform throughout the entire reaction zone, and the distinction between local and volume average photochemical reaction rates becomes mandatory. Experimental values of reaction rates obtained from concentration measurements performed in well-mixed reaction cells are, necessarily, average values. Consequently, for validation purposes, experimental results from these cells must be compared with volume averages of the mechanistically or empirically derived local reaction rate expressions. In this work it is shown that unless the rate is first order with respect to the photon absorption rate or the attenuation in the absorbing and/or scattering medium is kept very low, when the averaging operation is not performed, significant errors may be expected.

Optimal thermodynamic synthesis of thermal energy recovery systems

Abstract A thermodynamic method is proposed to generate sequences of optimal non-ideal thermal energy recovery systems (TERS). The two-fold objective of using the thermal energy recovered from hot process streams primarily as heating power and then as shaft power is considered. Shaft power generation might be a technical goal by itself. However, it always gives a way of measuring the possibilities for the original set of streams to be efficiently integrated with additional process streams. If T v is the absolute temperature of the steam utility and T o is that of the cold utility, then the total power recovered is assessed as G = Q E ( T v - T o )/( T v ) + τ, where Q E is the recovered heating power and τ is the shaft power that the system is able to generate. Each solution in a sequence of optimal non-ideal TERS will show: (i) the maximum value of G for the total exchange area A required and (ii) the maximum value for Q E , provided that condition (i) has already been met. Therefore, generation of shaft power is subsidiary to thermal energy recovery as heating power. It is shown that for optimal networks the rate of internal generation of entropy, σ, attains its minimum value compatible with constraints describing: (i) the transformations to be operated on the process streams and (ii) the subsidiary character of shaft power generation to thermal energy recovery as heating power. A systematic procedure is deviced to incorporate these constraints to the functional form for σ making use of the operating line concept. Optimal non-ideal networks are derived from a family of operating lines that are extremals (minimals) for the functional σ subject to the prescribed constraints. A procedure to evolve from this type of optimal networks to new ones showing a maximum for the ratio β = Q E / A for each given size of the exchange area, is also outlined. Applications to a test problem available in the literature and to an azeotropic distillation are also made.

Comparative analysis of pinch and operating line methods for heat and power integration

Two methods for approaching the problem of the optimal synthesis of heat-and-power cogeneration systems from a thermodynamic point of view are compared. The first one is the pinch method (Townsend and Linnhoff, 1983,A.I.Ch.E. J.29, 742–771) which is based on the pinch properties. The second one is the operating line method (Irazoqui, 1986, Chem. Engng Sci.41, 1243–1255) which considers the heat-and-power cogeneration as a unique, nonseparable problem. Different results for the appropriate placement of power-generating cycles can be derived by applying either method, particularly in the case of a “nose”-shaped grand composite curve. The efficiencies obtained with the operating line method are higher than those calculated with the pinch method, when both are applied to a dominant power load case.

Optimal synthesis of heat-and-power systems: the operating line method

Abstract The physical and mathematical models on which the operating line method (OLM) (H. A. Irazoqui, Chem. Engng Sci.41, 1243–1255 (1986); P. A. Aguirre, E. O. Pavani and H. A. Irazoqui, Chem. Engng Sci.44, 803–816 (1989)) for the optimal synthesis of heat-and-power systems is built, are discussed in depth. These models include the heat exchange ‘modes’ allowed and the general features of the type of solution sought in order to reach an optimal scheme for the total energy systems in chemical plants. A thorough development of the mathematical technique used to tackle the optimization problem is also made. This development comprises the derivation of the necessary and sufficient conditions for optimality.

Modelling and experimental validation of the radiation field inside an elliptical photoreactor

Abstract A rigorous modelling of a cylindrical photoreactor inside a cylindrical reflector of elliptical cross-section was performed and applied to a simple reaction in order to obtain information about its validity and limitations. The radiation field was modelled with the three-dimensional extended source approach. The radiation balance was coupled with a two-dimensional mass balance since azimuthal symmetry was assumed inside the reactor. Results indicate that the system can be precisely modelled in this way for small scale reactors but eventual commercial applications will necessarily need to remove the hypothesis of azimuthal symmetry. It was also found that the uranyl oxalate complex cannot be safely used as an actinometer in segregated flow photoreactors. Finally, it was confirmed that linear radiation emission models cannot be used when reflected radiation is an important contribution to the radiation field inside the reactor.

Optimal synthesis of heat-and-power systems with multiple steam levels

Abstract In this paper, the extension of the operating line method (Irazoqui, 1986, Chem. Engng Sci. 41 , 5) for the optimal synthesis of heat-and-power systems with dominant power load to the more general case of multiple steam levels is made. The thermodynamic meaning of the optimality region, obtained as a necessary condition for optimality, is also uncovered. An interesting feature of the optimal solution for the integration problem with multiple steam levels is that integration gaps arise. The optimal solution is compared to other solutions which appear as natural alternatives to it on the basis of the same value of the total area of heat exchangers and the same total power output. They all show lower values of their efficiencies to generate shaft power.

Dynamic correlations and microscopic fluid mechanics of a dense fluid

A method is developed for generating approximate numerical solutions to the coupled kinetic equations for the singlet distribution functions specific to a test particle and to a particle belonging to the surrounding solvent or background fluid. These kinetic equations are replaced with equivalent equations of motion for two sets of scalar valued quantities, each of which depends on time and a single spatial coordinate or displacement variable. These scalar valued quantities are contractions of tensor valued correlation integrals associated with a particular pair of momentum space basis functions. Formulas are given which relate these quantities to the correlation functions which are most directly connected to the observables generated by scattering experiments and by molecular dynamics computer simulations.

Kinetic Model of Photoautotrophic Growth of Chlorella sp. Microalga, Isolated from the Setúbal Lagoon

In this work, a kinetic expression relating light availability in the culture medium with the rate of microalgal growth is obtained. This expression, which is valid for low illumination conditions, was derived from the reactions that take part in the light‐dependent stage of photosynthesis. The kinetic expression obtained is a function of the biomass concentration in the culture, as well as of the local volumetric rate of absorption of photons, and only includes two adjustable parameters. To determine the value of these parameters and to test the validity of the hypotheses made, autotrophic cultures of the Chlorella sp. strain were carried out in a modified BBM medium at three CO2 concentrations in the gas stream, namely 0.034%, 0.34% and 3.4%. Moreover, the local volumetric rate of photon absorption was predicted based on a physical model of the interaction of the radiant energy with the suspended biomass, together with a Monte Carlo simulation algorithm. The proposed intrinsic expression of the biomass growth rate, together with the Monte Carlo radiation field simulator, are key to scale up photobioreactors when operating under low irradiation conditions, independently of the configuration of the reactor and of its light source.