Modeling in Chemical Engineering

Reduction of water activity aw can extend the shelf life and improve the quality of foods. After the optimal water activity has been selected, based on Karel’s aw-spoilage graphs, a simple decision scheme in this document helps to choose the best equation (“Law”) to calculate or adjust the water activity: for an aqueous one component  solution: Raoult’s and Norrish’ laws; spreadsheet “aw-Raoult-Norrish.xls”; or in case of an aqueous multi-component solution: Norrish’ and Ross’ laws; spreadsheet “Norrish-Ross.xls: aw calculations of a multi-component solution”. Both Excel spreadsheets, present in this document, simplify the tedious exponential aw calculations.
The water activity of a mixture of 2 to 5 solids can be predicted either by constructing the solids mixture sorption isotherm, or by using the Salwin equation. When applying the 3rd spreadsheet in this document, “Calculation Water Activity aw Solids Mixture.xls”, the  2 to 5 separate solids isotherms are converted into one new solids mixture sorption isotherm. Because the total water content of the solids mixture is known, the water activity of the solids mixture can be found from that new mixture isotherm. The calculations by the “aw Solid Mixture” spreadsheet are compared with aw findings from Salwin’s equation. Both aw values are in good agreement.
Several worked examples, for each of the 3 spreadsheets present, illustrate step-by-step the aw calculation of solutions and of solid mixtures.
Annex 1 lists the lowest water activity for growth and/or toxin production of many micro-
organisms in foods. Annex 2 shows the minimal aw for activity of the main food spoiling enzymes.

Reduction of water activity aW can improve the shelf life and the quality of foods. After
selecting the optimal water activity, a simple decision scheme helps to choose the best
equation (“Law”) to calculate or adjust the water activity: of an aqueous one component
solution (Raoult’s and Norrish’ laws), or of an aqueous multi-component solution (Norrish’ and Ross’ laws). For aqueous solutions of sugars, salts, electrolytes, and salt or fat replacers, three spreadsheets simplify the tedious exponential aW calculations: 
"aW-Raoult-Norrish.xlsx", and "aW-Pitzer equations.xlsx", for one component aqueous
solutions; spreadsheet "Norrish, Ross, Samapundo, Pitzer, and Baeza.xlxs" for
multi-component aqueous solutions. Sometimes, for a particular component, 2 or 3 aW equations are available; if possible, the equation’s  accuracy will then be reported.
The water activity of a mixture of 2 to 5 SOLIDS can be predicted either by constructing the solids mixture sorption isotherm, or by using the Salwin equation. When applying the
spreadsheet "Calculation Water Activity aW Solids Mixture.xlsx", the separate solids
isotherms are converted into one new solids mixture sorption isotherm. Because the total water content of the solids mixture is known, the water activity of the solids mixture can be found from that new mixture isotherm. Calculations with the "Solid Mixture" spreadsheet are validated by comparing its predicted solids mixture aW with the water activity, calculated by the Salwin equation. The two calculated solid mixture aW values are in good agreement.
Annex 1 lists the lowest water activity for growth and/or toxin production of many micro-
organisms in foods. Annex 2 shows the lowest aW for activity of the main food spoiling enzymes. Annex 3 gives many sources of Norrish k values; Annex 4 reports measured water activities for verification.
Several worked examples for each of the spreadsheets illustrate step-by-step the
aW calculation of aqueous solutions and of solid mixtures.

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.

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.

This is the complete finalized format for plant design and economic analysis mini project which emphasized on the phosphoric acid production. There are differences in terms of production since we split the 1st reactor into two separate reactors for better efficiency. This is as suggested by our respective lecturer since accumulating two different reactions in a single reactor will burden our calculations and produce a very complicated reactions and production.

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.

""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.
""

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.

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.

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.

Abstract Methods, parameterisations and models have been developed, which give insight in processes that are important for deposition of nitrogen compounds to the sea. This knowledge has been applied to the Kattegat Strait for which a nitrogen deposition of 960 kg N km-2 yr-1 was calculated with an atmospheric transport model.

We have studied the chemical evolution in the central core of a contracting cloud representing W3 IRS4. We modified the equation of temperature to satisfy the physical conditions of W3 IRS4. The chemical rate equations and the hydrodynamics 23 are integrated simultaneously. The contraction is followed from a very low density of n 5 10 cm to high core density of n 6 23 5 10 cm. The chemical evolution is studied for various chemical conditions, including both the effects of varying cosmic ray ionization rate and the effect of ion-dipole molecule collisions. The main results by using the more extensive chemical network with the most updating reaction rates show that the calculated fractional abundances are in agreement with observation at intermediate and enhanced cosmic ray ionization rate at high depletion of elemental atoms.

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.

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.

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.

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 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. Concerning the experimental results, the magnitude of the longitudinal dispersion and the extension of dead volumes is estimated for clean conditions and after a certain operating period under organic loading conditions. The results showed a considerable amount of longitudinal dispersion through the bed, which was very strong near the feeding point, indicating the occurrence of mixing and significant presence of dead zones and short-circuiting.

We have investigated the use of nanofiltration for treatment of effluent from the first alkaline extraction stage (called 'E1') of a bleached Kraft pulp plant. We report nanofiltration tests with a laboratory cross-flow unit 'CELFA P-28' to study the effect of the retentate flowrate, pH, and pressure, on permeate flowrate and pollutant removal efficiency. The data was used to predict the performance and approximate cost of a multi-stage nanofiltration unit at industrial scale. Its design was computer-optimized by the dynamic programming method.