Modeling in Chemical Engineering

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

Part of each feasibility study of a food production plant is to make an estimation of the “future” investment  costs in such a plant. In this document, the investment cost estimation method of Zevnik-Buchanan is explained, in 10 consecutive steps. The method, requiring a detailed plant flowsheet, can be executed manually by using graphs. However, calculation is more rapid and much simpler by using the Zevnik-Buchanan Excel worksheet, included in this document. For this worksheet, the Z-B graphs had to be converted into mathematical equations. These equations can be found in the corresponding graphs.
2 worked examples explain the basics of Zevnik-Buchanan's estimation method of plant cost investments: one about a 10 000 tons/year mozzarella factory, the other on a 1150 tons/year whole egg powder plant.
Calculations using the Zevnik-Buchanan graphs and equations are valid for the year 1996. To convert these 1996 figures to future estimated plant costs, the Chemical Engineering Plant Cost Indices (CE Plant Cost Index), from 1980 onward, have been included in Annex 2: both as a graph for easy extrapolation, and as a table.
For reference purposes, the 1986 Bartholomai investment costs of some 40 different food factories are listed in Annex 3.

""Part of each feasibility study of a food production plant is to make an estimation of the “future” investment costs in such a plant. In this document, three rapid investment cost estimation methods are explained: 1) the indexed 0.6 exponent method, in case your plant is “similar” to one of the 40 food plants, listed by Bartholomai; 2) the adapted Marouli method for complete food plants, if you only know the total production capacity of your plant, and 3) the adapted Marouli method for separate plant production sections, to be used if you have a plant flowsheet and you know the capacity of each of the main production sections of the food plant. Each of these 3 estimation methods can be executed manually, but calculation is rapid and simpler by using the 3 Excel worksheets, included in this document. Several worked examples explain the mathematics behind each of the 3 cost estimation methods; these examples should help to understand the basics of the calculations.
Usually, investment cost estimations are made for plants to be build in the near future. but are based on investment cost figures from the past, often with different production capacities. To convert past plant investment costs to future estimated plant costs, the Chemical Engineering Plant Cost Indices, from 1980 onward, are available, both as a table and as a graph. To convert plant production capacity from past to future capacity, the well-known 0.6 exponent rule is used.
Annex 1 discusses similar investment cost estimation methods for non-food plants, based on Perry’s (1985 and 1999) tables with past plant investment costs of many non-food factories.
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The Kozeny–Carman equation is a traditional permeability–porosity relationship which has been used in many models of real problems related to flows in porous media. In spite of this, some limitations of this well-known equation has motivated the conception of different versions, specialized for particular applications. In the present article, we deduce a three-parameter Kozeny–Carman equation obtained from a fractal structure involving the specific surface and the tortuosity of the porous medium. Here, a theoretical analysis indicates that the new equation is capable to generalize several models existent in the literature. Besides, parameter estimations fitting experimental data of different materials show that the present model can be used to describe the relationship between permeability and porosity of many materials, such as sandstones, sisal fiber mat and glass fiber fabrics.

The use of akernattve fuels from renewable vegetable sources has become increasingly widespread in recent yeats. In addition to other olternative fuels srch as ethanol, methanol or biogas (methane), fatty acid methyl esters are irs*v**singly being found on the market; these are eetso Imown as biodiesel or FAME (fotty acid '*aee&zyl esters). Fatty acid metlryl esters ire uswlly obtained from oil seeds and mainly used in their pureform or mixedwith corumtional dieselfuel in the transport sector. During manufacture the vegetable oil is trawesterified with methanol. This produces the metlryl esters of the fatty acids present in the oil together with glycerol as a by-pro&rct. Methanol concentrotion itself influence to some aspects in biodiesel such as conversion, yield, and quality. This paper discussed in daail. trFased on this study, as the methanol concmtration increased, which the yield of biodiesel and esther €{xrtent were also increased, while the total g€,3,cerol ond acid value were found to be decreased.

We present a numerical solution for the dead zone model which describes the solute transport in a subsurface and horizontal flow constructed wetland. This model is a system of two mass balance equations for two conceptual areas: the main channel and the storage zone. We use finite difference schemes to determine the numerical solution of the system and we study its convergence by presenting properties related to the stability and accuracy of the schemes.

For a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral Lyapunov function (PLF) implies structural (i.e., parameter-free) local stability. Global structural stability is ensured under the additional assumption that each of the variables (chemical species concentrations in CRNs) is subject to a spontaneous infinitesimal dissipation. This paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation, showing that the existence of a PLF structurally ensures global convergence if and only if the system Jacobian passes a structural non-singularity test. It is also shown that, if the Jacobian is structurally non-singular, under positivity assumptions for the system partial derivatives, the existence of an equilibrium is guaranteed. For systems subject to positivity constraints, it is shown that, if the system admits a PLF, under structural non-singularity assumptions, global convergence within the positive orthant is structurally ensured, while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise-linear-in-rate Lyapunov function.

This work introduces the Least Dot Products (LDP) method, a new algorithm for phase stability analysis of thermodynamic mixtures. Starting with the fact that tangent plane distance function (the objective function used in global stability tests) is, essentially, the dot product between the vector of compositions of a trial phase and the vector that describes the differences among the chemical potential of the components in the phases, our approach tries to obtain the least values of an auxiliary function that represents an appropriate dot product on a unitary sphere of the n-dimensional space, which is a good approximation for the stability test function. In agreement with the foundations of the Gibbs plane tangent criterion, the new algorithm simply tries to find points where the objective function is negative, which are not (necessarily) stationary points or global minima. Thus, our main contribution is not a new method for general nonlinear problems, or a rule-based termination criteria for a classical optimization method. Consequently, if such points do not exist, then LDP method is not capable to recognize the stability condition. To overcome this problem, we develop also a powerful safeguard algorithm, denominated Projected Simulated Annealing (PJSA) algorithm, which is obtained by projecting the Simulated Annealing algorithm onto the unitary sphere.In the present article, firstly we consider liquid–liquid equilibria at low or moderate pressures, where the excess Gibbs energy is described by NRTL or UNIQUAC models. Secondly, we address vapor–liquid equilibria at high pressures with cubic equations of state.To illustrate the performance of the new methodology, we use here 20 systems studied by other authors. Such problems possess 2–12 variables and constitute severe tests for many optimization methods. For some mixtures, we show that LDP method is capable of determining the instability condition using just two iterations.► We introduced the Least Dot Products (LDP) method. ► The LDP method is a new numerical paradigm for phase stability analysis. ► This method tries to find points where the tangent plane distance function is negative. ► These points are not (necessarily) stationary points or global minima.

We introduce a methodology to solve nonlinear systems of equations with bound constraints, and two or more roots. In order to find more than one root, this methodology uses an appropriate global optimization algorithm together with a polarization technique. Polarization modifies (successively after the determination of a new root) a merit function associated to the nonlinear system, creating repulsive regions in the neighborhood of the previous roots. We applied successfully the proposed methodology to solve hard nonlinear systems, including the double retrograde vaporization problem for binary systems of methane + n-butane.

The phenomenon of double retrograde vaporization (DRV) has been simulated using the group contribution equation of state coupled with the Michelsen computational procedures for calculating phase envelopes. This behavior was studied for a number of binary mixtures of near critical fluids with a low volatile component. For the binary systems ethane + limonene, ethane + linalool, methane + butane, and methane + pentane the "double-domed" and "S" shaped curves were successfully predicted and found to be in good agreement with the experimental information available. Prediction of DRV in a number of binary systems from different families further confirmed the idea of the generality of this behavior in all asymmetric mixtures. All results indicate that as the solute increases in molecular size, the composition at which the phenomenon of DRV starts to appear shifts to higher solvent concentration, while simultaneously covering a wider composition range. For the homologous n-alkane series in binary mixtures with C 1 up to C 5 as near-critical solvents, a correlation in the appearance of the phenomenon of DRV with the hard-sphere diameter of the solvent was observed. Although for each solvent, the lower limit of solute carbon number that shows DRV is easily estimated, the upper carbon number could not always be determined because the occurrence of liquid-liquid immiscibility interferes with the DRV phenomenon. In binary mixtures of CO 2 with homologous members of alkyl esters, no liquid-liquid immiscibility was predicted, so it was possible to determine both the lower and upper concentration bounds of DRV.

The phenomenon of double retrograde vaporization (DRV) has been simulated using the group contribution equation of state coupled with the Michelsen computational procedures for calculating phase envelopes. This behavior was studied for a number of binary mixtures of near critical fluids with a low volatile component. For the binary systems ethane + limonene, ethane + linalool, methane + butane, and methane + pentane the "double-domed" and "S" shaped curves were successfully predicted and found to be in good agreement with the experimental information available. Prediction of DRV in a number of binary systems from different families further confirmed the idea of the generality of this behavior in all asymmetric mixtures. All results indicate that as the solute increases in molecular size, the composition at which the phenomenon of DRV starts to appear shifts to higher solvent concentration, while simultaneously covering a wider composition range. For the homologous n-alkane series in binary mixtures with C 1 up to C 5 as near-critical solvents, a correlation in the appearance of the phenomenon of DRV with the hard-sphere diameter of the solvent was observed. Although for each solvent, the lower limit of solute carbon number that shows DRV is easily estimated, the upper carbon number could not always be determined because the occurrence of liquid-liquid immiscibility interferes with the DRV phenomenon. In binary mixtures of CO 2 with homologous members of alkyl esters, no liquid-liquid immiscibility was predicted, so it was possible to determine both the lower and upper concentration bounds of DRV.

The phenomenon of double retrograde vaporization (DRV) has been simulated using the group contribution equation of state coupled with the Michelsen computational procedures for calculating phase envelopes. This behavior was studied for a number of binary mixtures of near critical fluids with a low volatile component. For the binary systems ethane + limonene, ethane + linalool, methane + butane, and methane + pentane the "double-domed" and "S" shaped curves were successfully predicted and found to be in good agreement with the experimental information available. Prediction of DRV in a number of binary systems from different families further confirmed the idea of the generality of this behavior in all asymmetric mixtures. All results indicate that as the solute increases in molecular size, the composition at which the phenomenon of DRV starts to appear shifts to higher solvent concentration, while simultaneously covering a wider composition range. For the homologous n-alkane series in binary mixtures with C 1 up to C 5 as near-critical solvents, a correlation in the appearance of the phenomenon of DRV with the hard-sphere diameter of the solvent was observed. Although for each solvent, the lower limit of solute carbon number that shows DRV is easily estimated, the upper carbon number could not always be determined because the occurrence of liquid-liquid immiscibility interferes with the DRV phenomenon. In binary mixtures of CO 2 with homologous members of alkyl esters, no liquid-liquid immiscibility was predicted, so it was possible to determine both the lower and upper concentration bounds of DRV. .ar (E.A. Brignole), cor.peters@tnw.tudelft.nl (C.J. Peters).

A B S T R A C T Using Density Functional Theory (DFT) calculations, we studied the electrochemistry of polyoxome-talates (POMs), specifically the redox properties of Mn in tri-Mn-substituted W-based Keggin ions. For direct comparison with recent cyclic voltammetry results [J. Friedl et al. Electrochim. Acta, 141 (2014) 357], we estimated the reversible half-wave potentials of proton-and cation-coupled electron transfer for Mn(IV/III) and Mn(III/II), respectively. The calculated reversible potentials agree well with experiment, reproducing the trend with pH for Mn(IV/III). For adequate DFT energies, it is crucial to apply a reliable description of the electrolyte environment of the POM, accounting also for their rather high charges, up to À7 e. To this end, we included the Li + counterions, required for charge neutralization, directly in the quantum chemical models which were embedded in a polarizable continuum. We explored various arrangements of the Li + ions around the POMs and their effect on both structural parameters and electrochemical properties of the POMs. Hybrid functionals (TPSSh, B3LYP, PBE0) overestimate the experimental reduction potentials: the larger the exact-exchange contribution, the larger the resulting reduction potential. The best agreement with experiment is achieved with the PBE approach, likely due to fortuitous error cancellation. The results of the present work indicate that a more sophisticated (atomistic) representation of the electrolyte environment will be beneficial for predicting redox potentials in better agreement with experiment.