Component Material Balances Research Articles

Creation of an identifier database for the ammonia synthesis computer control system

The object of research is the control system of the synthesis department of the large-tonnage ammonia production unit of the AM-1360 series. An analysis of the functioning conditions of the synthesis department was carried out. The significant influence of the content of inerts in the synthesis cycle on the energy efficiency of ammonia production is shown, the optimal value of which depends both on the accepted level of prices for energy carriers and on the method of using purge gases. The need to create a computer-integrated control technology to optimize the use of purge gases is established. The function of the identifier of such a control technology is defined, namely, continuous refinement based on current information about the state of the main sections of the synthesis department, such as the synthesis column, primary and secondary condensation. The operation of these stations takes place in the conditions of seasonal and daily changes in the heat load, which causes parametric uncertainty of such parameters of the connection of the mathematical model as the concentration of ammonia in the circulating gas at the outlet of the stations listed above. Numerical assessment of these uncertainties according to the results of analytical studies for such technological objects is most often performed using stochastic approximation methods. Let’s note that the significant inertia of the objects of the synthesis department under certain conditions makes it impossible to adapt the parameter to its actual value. An algorithmic base has been created for the formation of an information array of the identifier of the computer-integrated control technology of the ammonia synthesis department, which ensures the separation of transient modes under conditions of uncertainty and allows to perform the task of identifying processes in the synthesis column, in the primary and secondary condensation units. The proposed algorithm allows to perform convergence in the department both on the general and on the component material balances. The algorithm is implemented in the MatLab application program package and tested by means of simulation based on experimental data of industrial operation of AM-1360 series ammonia synthesis units.

A Novel Approach to Modeling Biomass Pyrolysis in a Fluidized Bed Reactor

A novel approach to simulating biomass pyrolysis in a fluidized bed of mostly inert material is presented. The bed is assumed to be externally heated, although simulation of autothermal operation with partial oxidation of the products is a future objective. Combining pyrolysis reaction kinetics developed by the CRECK Modeling Group and a previously published component properties model, material and energy balances are closed by tracking the residence time of biomass particles without regard for their exact spatial distribution. The model is used to simulate a pilot-scale fluidized bed pyrolysis process being developed at Iowa State University, and model predictions are compared with experimental results for red oak and corn stover feedstocks. The results are in general agreement, with the model typically predicting more noncondensable gas and less low-boiling liquid products. The differences are ascribed to the limitations of the kinetics model. This model provides a rigorous energy balance for fluidized bed pyrolysis processes that can be incorporated into commercial flowsheet models with the capacity for future addition of partial oxidation reactions and implementation of improved kinetics models.

Mathematical modelling of the reaction of condensation telomerization and the investigation of the model

A mathematical model of the distribution of mixture components in the equilibrium condensation telomerization is developed depending on the ratio of the amounts of monomers and telogen, as well as the number of HX as regulating parameters, the computer implementation of the model is carried out, and its study is carried out by numerical simulation. The model is based on the well-known schematic diagram of the flow of the condensation telomerization process under the assumption of equal reactivity of the same functional groups (Flory principle). Based on the analysis of the flow pattern of the process, 6 structural elements are identified, reproducible at each stage associated with an increase in the degree of polymerization based on 4 basic components. It is proved that the equilibrium concentrations of these elements, depending on the polymerization degree, depend on the equilibrium concentration of products with a degree of polymerization 1 and are described by infinite geometric progression with the same denominator. According to the physical content of the task, this progression must be convergent. Equations of material balance of components are contained in the form of a system with 4 equations containing infinite sums. It is possible to minimize these sums using the properties of geometric progressions and to obtain a closed system with 4 nonlinear equations for the equilibrium concentrations of the base components. The Monte Carlo method is used to study the features of the numerical solution of the system of equations of the model. It is found that with a random choice of initial approximations of solutions from an admissible region, the system contains 4 roots, of which 2 contain positive and negative components and are false, and 2 have completely positive components. A valid criterion for finding a real root has a physical meaning based on the calculation of the denominator of a geometric progression. The possibilities of practical use of the model are discussed

Partition of valuable components between slag and metal in the blast furnace operating with high chromium, vanadium, titanium, magnetite ores

In order to master the partition between metal and slag for high chromium vanadium titanium magnetite in ironmaking process, the same batch of sinter, pellet, hot metal and slag were investigated mainly from two viewpoints of phase composition change and distribution of valuable components in this study. Chemical analysis, XRD and SEM-EDS analysis, material balance and distribution of valuable components reveal that the total input-output amounts of valuable components are nearly balanced under the stable operation condition. 98.60% of iron, 86.71% of vanadium, 83.73% of chromium and only 6.48% of titanium have passed to hot metal. The distribution of titanium and silicon between hot metal and slag was investigated, which is in accordance with the previous studies in the laboratory condition. The phase composition change process of vanadium is V2 O3 → [V]. The reduction process of chromium oxide is Cr2 O3 → [Cr]. The titanium oxide is partially reduced into the hot metal in the hearth by the reaction: TiO2 → [Ti], then the dissolved titanium can easily react with C and N2 forming Ti(C,N).

Material Balance of Olive Components in Virgin Olive Oil Extraction Processing

Processing of olive fruits using a three-phase extraction system for the production of virgin olive oil was analyzed to clarify the material balance of olive fruit components, i.e., oil, water, carbohydrates, proteins, minerals and polyphenols. The estimated total olive material balance based on mass flow indicated a final oil extraction yield of around 83.3%, with an initial olive fruit mass flow of 500 kg/h. The remaining oil was discharged as a by-product, mainly in olive cake (8.9%) and olive mill water (7.8%). The material balance of carbohydrates showed that the majority were discharged in olive cake (73.3 kg/h) and olive mill water (27.7 kg/h). The material balance of polyphenols, the most important functional compounds in olives, was determined because of their importance to olive oil chemical stability. Results showed an increase in polyphenols content during malaxation operation (17.6%), which was correlated with several enzymatic reactions directly reflected in the composition of virgin olive oil.

A new approach for global optimization of a class of MINLP problems with applications to water management and pooling problems

AbstractOne of the biggest challenges in solving optimization engineering problems is rooted in the nonlinearities and nonconvexities, which arise from bilinear terms corresponding to component material balances and/or concave functions used to estimate capital cost of equipments. The procedure proposed uses an MILP lower bound constructed using partitioning of certain variables, similar to the one used by other approaches. The core of the method is to bound contract a set of variables that are not necessarily the ones being partitioned. The procedure for bound contraction consists of a novel interval elimination procedure that has several variants. Once bound contraction is exhausted the method increases the number of intervals or resorts to a branch and bound strategy where bound contraction takes place at each node. The procedure is illustrated with examples of water management and pooling problems. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2320–2335, 2012

Comparative control study of a simulated batch rectifier

This article proposes a nonlinear control strategy for a batch rectifier. The hybrid control strategy comprises a state estimator, namely Luenberger-like nonlinear estimator (LNE) and the feedback linearizing controller (FLC). The observation scheme aims to estimate the imprecisely known parameter based on the available measurement. For the representative distillation unit, the state predictor is formulated using only a component material balance equation around the condenser–reflux drum system. It clearly indicates the existence of a process/model mismatch and this discrepancy is efficiently taken care of by the corrector part of the LNE. In the subsequent phase, the FLC is synthesized for the example system. The derived nonlinear FLC–LNE controller shows better performance compared to a traditional proportional integral (PI) law. The simple structure, straightforward design and good performance make this nonlinear controller attractive for online use.

Mathematical modeling of sorption preconcentration in flow analysis system

A mathematical description of all steps of sorption preconcentration in flow analysis systems is developed based on equations of material balance, mass transfer, and equilibrium distribution of micro components. The description of the sorption step allows calculation of the analyte distribution throughout the column. Further, the distribution is used as the initial boundary conditions for description of the desorption step. For practical calculation, a system of model equations is formulated and adopted to Comsol software. The numerical values of the parameters are derived from experimental data using a stepwise approximation method to achieve a minimal spread between the theoretical and experimental curves. An algorithm is developed for estimation of the confidence intervals for the parameters of the model based on the dispersion of the experimental data.

Development of a flowsheet for iodine–sulfur thermo-chemical cycle based on optimized Bunsen reaction

Based on the Bunsen reaction process whose operating conditions are optimized to yield an over-azeotropic HI liquid solution, we devised a new flowsheet of iodine–sulfur thermo-chemical cycle. A highly enriched hydrogen-iodide gas can be generated through a series of processes of liquid–liquid separation of product mixture from Bunsen reaction and flash of over-azeotropic HI solution. Operating temperature and pressure for HI enrichment need not to be increased as high as those for existing flowsheets; as a result, the operating conditions become less corrosive. Chance of pipe clogging due to iodine solidification is low because there is no process where iodine is concentrated that high. Enrichment of HI through spontaneous liquid–liquid separation and simple flash processes avoiding complicated separate process is considered to be an additional benefit. Analysis of overall and component material balances showed that excess amount of feed to each process to get a desired output depends on the efficiency of flash and decomposition processes. Compared to previous ones, the proposed flowsheet requires more recirculation flows throughout the whole cycle mainly because only a portion of HI content exceeding the azeotrope is allowed to evaporate in the flash without employing a separate HI enrichment process. Thermal efficiency of the proposed flowsheet was evaluated, together with a series of parametric analyses for the sensitivity to key operating parameters and component performances. It was observed that the thermal efficiency can be raised above 60% at optimal condition.

Nonlinear Exponential Estimator Design for a Distillation Column

This article presents the design of an exponential state estimator for a distillation column. The proposed algorithm mainly estimates the imprecisely known parameters based on the available measurements. For the example distillation column, the nonlinear state estimator is formed with two component material balance equations; one is around the condenser-reflux drum system and the other one is around the reboiler-column base system. As a result, there is an excessive process/model mismatch. In this situation, the proposed scheme estimates the augmented states with sufficient accuracy. The simulation experiments have been performed to investigate the convergence ability of the estimator. The less computational requirements and simple design make the estimator attractive for online use.

Mathematical modeling of gas–liquid membrane contactors using random distribution of fibers

This work presents a mathematical model for gas absorption in microporous hollow fiber membrane contactors by using a random distribution of fibers. The chemical absorption of carbon dioxide into aqueous amine solutions and sulfur dioxide into water were simulated by this model. The nonlinear mathematical expressions of the component material balance for the liquid, membrane, and gas were solved simultaneously by using a numerical method. The results from the model were compared with four sets of different experimental data in the literature. In addition, the contactors were modeled based on the assumption of regular arrangement of fibers in the shell side by using Happel's free surface as well as plug flow models. The plug flow model was employed to compare the various available equations in the literature for the shell side mass transfer coefficient. The results indicate that the channeling of gas in the shell side decreases the efficiency of contactor significantly. It was found that the random distribution of fibers is a suitable method to simulate the commercial modules. The results also indicate that, the regular Happel's free surface model and the plug flow model are more suitable for handmade modules. The influence of shell side channeling on the contactor performance were investigated in different fiber packing densities, and in various gas and liquid flow rates.

Description of kraft cooking and oxygen–alkali delignification of bamboo by pulp and dissolving material analysis

The oxygen delignification of two bamboo ( Bambusa procera) kraft pulps with kappa numbers of 13.6 and 20.0 were studied under typical conditions. Based on detailed analysis data on both the kraft and oxygen-delignified pulps and the corresponding spent liquors (black liquors and oxygen stage effluents), three yield and four selectivity estimation methods, utilizing component material balances, were tested resulting in the value ranges 96.2–97.9% and 43.5–60.4%, respectively, for oxygen delignification process studied. The traditional selectivity using the viscosity and kappa number relation was 66.9–68.4%. The studied bamboo kraft pulps behaved typically as birch kraft pulps during oxygen delignification, resulting, for example, in similar carbohydrate-derived degradation products.

Ionic transport through ion-exchange and bipolar membranes

Problems of steady-state and non-steady-state multi-component ion transport through ion-exchange and bipolar membranes and adjacent diffusion layers are considered. Equations of material balance of electrolyte components and the Poisson equation are used as the mathematical model. An efficient numerical method providing splitting of equations of material balance of electrolyte components and the Poisson equation is proposed. The method requires no explicit consideration of interfaces and the use of Donnan equations; it provides exact fulfillment of boundary conditions both for the mode of constant current density and for the mode of constant voltage. The following results of simulating the ion transport through ion-exchange and bipolar membranes and adjacent diffusion layers are presented: the distributions of concentrations, electrical potential, charge, and partial current densities and the voltammograms of electromembrane systems.

Property integration: Componentless design techniques and visualization tools

AbstractStandard techniques for process design are based on tracking individual chemical species. Component material balances are at the heart of any design approach. Nonetheless, many design problems are not component dependent, but are driven by properties. Recently, the concept of clustering has been introduced to enable the conserved tracking of surrogate properties. Hence, the process design can be optimized, based on integrating properties instead of chemical species. Systematic techniques have been developed for this new paradigm of property integration to illustrate its applicability. Property integration is defined as a functionality‐based, holistic approach to the allocation and manipulation of streams and processing units, which is based on tracking, adjusting, assigning, and matching functionalities throughout the process. Revised lever arm rules are devised to allow optimal allocation while maintaining intra‐ and interstream conservation of the property‐based clusters. The property integration problem is mapped into the cluster domain. This dual problem is solved in terms of clusters and then mapped to the primal problem in the property domain. Several new rules are derived for graphical techniques. Particularly, systematic rules and visualization techniques for the identification of optimal mixing of streams and their allocation to units. Furthermore, a derivation of the correspondence between clustering arms and fractional contribution of streams is presented. This correspondence is employed to minimize the usage of fresh resources by minimizing cluster arms. The selection of optimal values of the augmented property index is also developed. Finally, graphical tools are devised for task identification of property adjustment. The new techniques are illustrated using a case study on fiber recovery in papermaking. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1854–1869, 2004

A novel framework for simultaneous separation process and product design

The objective of this paper is to introduce a systematic framework for simultaneous solution of process/product design problems related to separation. This framework is based on the recently developed property clustering approach that allows one to perform design calculations on a component-free (or composition-free) basis. Removing the composition dependency from the design problem enables the simultaneous consideration of process and product selection and optimization. The clustering concept is based on the observation that properties, unlike mass, are not conserved and consequently they cannot be tracked among process units without performing component material balances. To overcome these limitations the use of property-based clusters has been proposed. The model derivations and reformulations to cluster-based models are presented and the usage highlighted through a simple proof of concept example and a case study.

Behavior of bromine on the thermal decomposition of paper-based phenolic laminate wastes

We investigated the thermal properties and behavior of bromine on the thermal decomposition of paper-based phenolic laminate wastes containing polybrominated flame retardants. The thermal properties of the phenolic laminate wastes were measured with a thermogravimeter and a conduction-type scanning calorimeter (TG-CSC). The weight loss of the wastes on thermal decomposition was mainly in three phases between 40°C and 600°C. The enthalpy (ΔH) of the thermal decomposition was 104 cal/g. The material balance of the decomposition components was measured with batch-type thermal decomposition equipment. The ratios of carbon residue, liquid, and gas on decomposition at 800°C in a vacuum were 37 wt. %, 48 wt. %, and 15 wt. %, respectively. The bromine contents in the carbon residue and liquid were less than 0.02 wt. % and 10 wt. %, respectively. These results are useful both in the carbonization process of these wastes and in the application of carbon residue as carbon materials.

Total Reflux Simulation of Packed Column Distillation.

This paper presents a simulation algorithm with a rate-based model for a packed distillation column at total reflux.The proposed algorithm consists of 1) composition and temperature profile calculation, which is slightly modified from the one for steady-state continuous distillation at finite reflux, and 2) composition correction for accelerating convergence with the overall θ method based on the component material balance considering liquid hold-up within the distillation column.Simulation results are compared with the experimental results of a ternary system obtained from a 0.21 m diameter packed distillation column. Fairly good agreement is obtained, though proper evaluation of the effective interfacial area and liquid hold-up distribution is essential for better simulation.

A Relaxation Method for Solving Reaction Problem in an Isothermal Tubular Reactor with One-Dimensional Eddy Diffusion.

A numerical method is proposed for solving an isothermal equimolar vapor phase parallel reaction problem in a tubular reactor with one dimensional eddy diffusion under the boundary conditions given by Danckwerts.This problem is described by simultaneous second order ordinary differential equations, and is transformed to a set of nonlinear simultaneous algebraic equations by expansion using the central finite difference operator. The Newton-Raphson method has been frequently used to solve these equations in spite of the difficulties of complicated derivation of Jacobian matrix and selecting adequate initial values.The proposed method is based on the relaxation method and consists of two calculation loops i) to correct the compositions of segmentation points of a reactor using a θ method with component material balances and ii) to repeat the point-by-point calculation in the sequence shown by Mori et al. in the solution of multistage, multi-component distillation problems. The method provides stable solution with a brief algorithm regardless of the number and rate equation of reactions, and is less sensitive in selecting initial values. The usefulness of the method is demonstrated by some numerical examples.

Development of a software for simulating separation processes using a nonequilibrium stage model

This paper is concerned with the computational aspects of countercurrent multicomponent separation processes using a nonequilibrium stage model. The developed program solves the component material and energy balance relations for each phase together with mass and energy transfer rate equations and equilibrium equations for the interface. The program is formulated in such a way as to make the describing equations and the method of solving them independent of the methods used to predict the vapor and liquid multicomponent mass transfer coefficients and heat transfer coefficients as well as physical properties like density, viscosity, binary diffusion coefficients, component specific heats and thermal conductivity, and the thermodynamic properties of the system. The composition and temperature profiles predicted by the program during the multicomponent distillation in bubble-cap-tray columns can be compared with the profiles given by the simulation using a conventional equilibrium stage model. The comparison permits the deduction of a methodology to predict more realistic stage efficiencies which can allow the utilization of the equilibrium stage model. A first attempt is being made using a new procedure based on the O'Connell correlation.

Batch extractive distillation under constant reflux ratio

The process of batch extractive distillation may provide the advantages of both batch and extractive distillation. So far this process has not been applied at all probably due to its complexity. An algorithm and a computer program were developed for simulating the experiments of a batch extractive distillation process (separation of acetone and methanol on a pilot-plant column containing 32 bubble cap trays applying water as solvent, the reflux ratio is kept constant) on a PC/AT/486. For the integration of the set of nonlinear differential equations (component material balances) the Runge-Kutta method was used. For saving computation time a 2-D linear interpolation method was applied for the ternary mixture when calculating VLE. The experimental and calculated results are compared. Thqe influence of the operational parameters on the process was studied by simulation. Calculations were carried out for another (nonazeotropic, low relative volatility) mixture with a new professional program “PROSIM BATCH”.