Column Operation Research Articles

Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods

We formulate a more straightforward, symmetry-based technique for manually computing the determinant of any n×n matrix by revisiting Dodgson’s condensation method, as well as strategically applying elementary row (column) operations and the definition and properties of determinants. The result yields a more streamlined algorithm that is generalized through formulas and employs a smaller number of operations and succeeding matrices than the existing methods.

Preparation of waste face masks modified with MnO2/poly(m-phenylenediamine) as a novel adsorbent for hexavalent chromium removal: Comprehensive batch and column study

Single-use surgical face masks (SFM) have become one of the most used personal protective equipment (PPE) for preventing the transmission of diseases, especially COVID-19. However, the environment is being threatened by the huge amount of plastic waste generated by this material. In this study, a novel environmentally-friendly in-situ-surface polymerization method was employed to modify the surface of SFM with m-phenylenediamine (mPDA) for removing hexavalent chromium. The synthesized adsorbent was characterized by Field Emission-Scanning Electron Microscopy (FESEM) and Fourier Transform Infrared Spectroscopy (FTIR). The investigations showed that the polymer and oxidant solution can be reused for several cycles, which was not possible in the conventional chemical polymerization method with ammonium persulfate (APS). The influence of various variables on the adsorption process was assessed and the optimum results was reported (adsorbent dosage: 3 g L−1, contact time: 60 min, pH: 2). The modeling investigations demonstrated that the process is followed by pseudo-second-order kinetic and University of Tehran (UT) isotherm model's assumptions, respectively. The obtained thermodynamic parameters at the investigated temperatures revealed the spontaneity and endothermic nature of Cr(VI) adsorption on the modified adsorbent. The column study was conducted and the impact of the flow rate and the feed concentration of Cr(VI) were evaluated. The experimental findings were analyzed using the Thomas model to discover how the concentration changes over time in the column operation. It was revealed that when the flow rate rose, the service volume declined.

A FAST COMPUTATION FOR EIGENVALUES OF CIRCULANT MATRICES WITH ARITHMETIC SEQUENCE

In this article, we derive simple formulations of the eigenvalues, determinants, and also the inverse of circulant matrices whose entries in the first row form an arithmetic sequence. The formulation of the determinant and inverse is based on elementary row and column operations transforming the matrix to an equivalent diagonal matrix so that the formulation is obtained easily. Meanwhile, for the eigenvalues formulation, we simplify the known result of formulation for the general circulant matrices by exploiting the properties of the cyclic group induced by the set of all roots of as the set of points in the unit circle in the complex plane, and also by considering the specific property of arithmetic sequence. Then, we construct an algorithm for the eigenvalues formulation. This algorithm shows a better computation compared to the previously known result for the general case of circulant matrices.

Fixed-Bed Studies of Landfill Leachate Treatment Using Chitosan-Coated Carbon Composite

The feasibility of a chitosan-coated coconut-shell (CS) carbon composite for landfill leachate treatment in a fixed-bed study was investigated in terms of COD and NH3-N removal. The surface of the composite was characterized using SEM, FT-IR, and XRD to assess any changes before and after column operations. To enhance its cost-effectiveness, the saturated composite was regenerated using NaOH. The results showed that the composite had significantly better removal of both COD and NH3-N, as compared to CS and/or chitosan (p ≤ 0.05; ANOVA test), respectively. The breakthrough curve obtained from the fixed-bed studies exhibited an ideal “S” shape. The breakthrough points for the adsorbents followed the order of CS at BV 76 < chitosan at 200 BV < composite at BV 305. It was also found that a low flow rate and deeper bed depth of the packed adsorbent were necessary for achieving optimal column operations. The composite achieved 96% regeneration in the first cycle. However, even with the enhanced adsorption of target pollutants by the composite through chitosan coating, the treated effluents still could not meet the required COD and NH3-N effluent limits of less than 200 and 5 mg/L, respectively, as mandated by legislation. Nonetheless, the findings suggest that low-cost composites derived from unused resources can be employed as effective adsorbents for wastewater treatment.

Automated detection of loading and flooding points in packed columns

Predictive correlations for packed distillation and absorption columns usually cannot account for changes in operating limits due to phenomena such as fouling. A method for detection of loading and flooding points even under altered operating conditions would therefore be highly desirable. In this work, a new approach for real-time detection of packed column loading and flooding points is introduced. The method utilises Fourier analysis of pressure drop data. Pressure drop fluctuations occurring even under steady-state conditions are sampled and treated with Fast Fourier transform (FFT) to derive the corresponding frequency spectra. Results of examinations with three structured packings (RSP 250Y, RMP N 250X, RMP N 250Y) conducted at three liquid loads each show that operating regions (below loading point, loading point, loading region, flooding point) can be identified from the obtained frequency spectra. Starting at the loading point, certain amplitudes within the spectra grow and increase up to the flooding point. This behavior is consistent for all examined packings. The results from this study suggest that the proposed approach could support column operation as an additional monitoring tool that is low in cost and not reliant on additional measurements besides pressure drop.

Optimized conditions for the design and operation of a vacuum distillation column for the purification of crude glycerol from biodiesel production

AbstractDue to the growth in global demand for biodiesel, there is a tendency for the volume of its main by‐product, glycerol, available on the market to increase. This has led to a search for new uses for this by‐product and the development of new processes that use glycerol as a raw material because it has wide industrial applications. However, to be used in many of these processes, the glycerol must go through a purification stage before reaching the purity required for the application (which can reach 99.7% w/w). Taking this into account, the optimization of the parameters for the main glycerol purification stage (vacuum distillation) is essential to reduce the cost of this stage as much as possible. In this article, optimization of the vacuum distillation column was carried out using an artificial neural network (ANN) and a genetic algorithm (GA) together. With the optimization, it was found that four theoretical stages of equilibrium (separation) is the optimal value, in economics terms, for the distillation column on an industrial scale, leading to better performance (in terms of glycerol purity) than patents that used a smaller number of theoretical stages and an equal performance in relation to the patents that used a greater number of stages, which in this case reduces the cost with the size of the column. This result helps to increase the financially viability of using glycerol as a raw material, which can make several processes cheaper, thus generating greater added value to this sustainable by‐product. © 2023 Society of Industrial Chemistry and John Wiley & Sons Ltd.

Progress Toward a Comprehensive Model for Mass Transfer in Structured Packings

Significant effort has been devoted to the study of mass transfer in sheet metal structured packings over the past half century. A number of mass transfer correlations have appeared in the literature as a result of those efforts. Unfortunately, none of these correlations has shown itself to be reliable over the full range of chemical systems, column operating conditions, and packing topologies encountered today. In an attempt to rectify some of the shortcomings of earlier correlations for sheet metal structured packings, we have employed a new data analysis methodology which simultaneously fits ⟨HETP⟩ data and mass transfer area data. The correlation we report upon here includes 444 ⟨HETP⟩ values from a variety of systems, operating pressures, and packing designs, along with 409 mass transfer area measurements. We demonstrate that this correlation outperforms all others while remaining simple enough to implement in process simulation software.

Adsorption of Phenol and Zinc as Dual Contaminants in Groundwater on Flood Plain Deposit Aquifer: Kinetic, Thermodynamic, and Column Operation Studies

Adsorption of Phenol and Zinc as Dual Contaminants in Groundwater on Flood Plain Deposit Aquifer: Kinetic, Thermodynamic, and Column Operation Studies

The unexpected weirdness of rate-based simulation of some high-pressure column operations

Diffusion is the process by which molecules move. One way to model multicomponent diffusion is with a version of Fick’s law: (J) = - [D] d(c)/dz where [D] is a matrix of multicomponent diffusion coefficients. [D] is the product of two other matrices, one of which involves partial derivatives of the fugacity or activity coefficients. It is usually the case that all of the elements on the main diagonal of [D] have a positive value. Wambui Mutoru and Firoozabadi (2011, 2012) showed that CO2-rich and N2-rich hydrocarbon systems could have main diagonal elements of [D] that are negative. Using rate-based column simulations, we have found that these negative main diffusion coefficients readily occur in some high-pressure distillation operations. We investigate these processes in more detail and explore the consequences for the design and operation of columns in which this phenomenon is predicted to occur.

System efficiency and power assessment of the all-aqueous copper thermally regenerative ammonia battery

Thermally regenerative ammonia batteries (TRABs) use low-temperature (T < 100 °C) heat to provide stationary energy and power with higher power densities and efficiency relative to other waste heat devices. TRABs are an active area of research in waste heat devices, but currently there is little consensus on what aspect of the system is limiting TRAB performance and what maximum efficiencies are possible. Experiments and numerical models were used here to examine the sensitivity of the battery and distillation column in a TRAB system to key operating variables, thereby establishing practical limits and identifying focus areas for improving performance. Battery power was eight times more sensitive to ohmic losses than kinetic and mass transfer losses, regardless of the operating temperature, and the peak power density was simulated to be 18.8 mW cm−2 at 75 °C. Theoretical energy efficiency limits were defined for a series of ammonia concentrations and operating pressures, ranging from 5 − 12%, which is 2–3 times higher than previous experimental estimations. Atmospheric pressure column operation used a larger amount of waste heat compared to sub-atmospheric pressure. It is estimated that the volume of the battery would take up 9.2 m3 for every 1% of the power output of a natural gas turbine, but with realistic improvements to cell conductivity, the size would reduce to 2.5 m3. The results presented in this work will help streamline future development by focusing on minimizing ohmic losses and provide specific data for full system evaluation of future TRABs.

Weld Repair Technique for Petroleum Product Pipeline in Extreme Conditions of Prolonged Thermal Cycling

The paper presents the results of experimental research on the development of a repair technique for a pipeline transporting hydrogen mixed with petroleum vapors, which has been in operation for 25 years at Mozyr Oil Refinery, the largest oil enterprise of the Republic of Belarus. The failure of this pipeline was caused by a crack formed in the weld root and its propagation along the fusion line of the heterogeneous weld joint. The developed technique made it possible to prevent further crack propagation without interrupting the refinery fractionation column operation. Welding of the main weld should be performed on a previously deposited damping layer. The damping layer must be deposited by using welding materials, the welding method and the technique that lead to creating a nonoriented dendritic structure. For this purpose, a welding material that has an energy of crack initiation and propagation greater than the energy of crack propagation in the base metal must be used. The composition of the weld must include chemical elements that inhibit the intensity of diffusion processes and increase the strength of the interatomic forces of the austenitic matrix at the pipeline operating temperature.

A Model of Froth Flotation with Drainage: Simulations and Comparison with Experiments

The operation of a froth flotation column can be described by a nonlinear convection–diffusion partial differential equation that incorporates the solids–flux and drift–flux theories as well as a model of foam drainage. The resulting model predicts the bubble and (gangue) particle volume fractions as functions of height and time. The steady-state (time-independent) version of the model defines so-called operating charts that map conditions on the gas and pulp feed rates that allow for operation with a stationary froth layer. Operating charts for a suitably adapted version of the model are compared with experimental results obtained with a laboratory flotation column. Experiments were conducted with a two-phase liquid–bubble flow. The results indicate good agreement between the predicted and measured conditions for steady states. Numerical simulations for transient operation, in part for the addition of solid particles, are presented.

Optimization of technological regimes of the deisopentanizer column for the preparation of the feed stream of the low-temperature isomerization unit PGI-DIG/280-NK

Raw fractions used in isomerization plants contain isopentane, which is the target product, and its presence in the feed as “ballast” occupies the useful volume of the reactor. To optimize the composition of processed raw materials, a number of enterprises have included a deisopentanizer column in the technological scheme. The paper evaluates the possibility of optimizing the technological regimes and design parameters of a deisopentanizer for a low-temperature isomerization unit that does not have a column in the technological scheme for extracting isopentane from the composition of the feedstock. The studies were carried out using the Honeywell UniSim Design modeling system. The properties of the fraction components were calculated using the Peng-Robinson method. Calculations were made for two types of raw materials containing 8.7÷19.7% wt. isopentane. The performed calculations established that in order to achieve almost complete recovery of isopentane in the feed stream from the hydrotreating section, the distillation column should contain 63 theoretical plates, and the minimum reflux ratio should be Rmin = 12.3. At the same time, the presence of normal pentane in the distillate of the column will not exceed 0.07% wt., and in the bottom product, the content of isopentane will also not exceed 0.07% wt. The operation of a distillation column is simulated, containing 80 plates (the efficiency of the contact device is 0.8), a feed plate is 33. The feedstock consumption is 62550 kg/h, the temperature is 40°C and the pressure is 294.2 kPa. The convergence of iterative processes by the Honeywell UniSim Design environment was obtained using active specifications: the content of isopentane in the cube is 0.0007wt. share and pentane in the distillate 0.0007wt. share. The obtained technological modes provide almost complete extraction of isopentane from the composition of the raw material, namely by 99.37÷99.7%, while for industrial conditions it is essential to implement the calculated temperature profile along the height of the column. The possibility of using a column with the same diameter in its exhaustive and strengthening parts is shown.

Determination of the bearing capacity of encentrally compressed concrete filled steel tubular columns on the basis of the deformation theory of concrete plasticity

Objective. The article proposes a method for finite element analysis of pipe-concrete columns in a physically nonlinear setting by reducing a three-dimensional problem to a twodimensional one based on the hypothesis of plane sections.Method.The equations of the theory of plasticity of concrete by G.A. Geniev are used. The technique was tested by comparing the solution with a calculation in a three-dimensional setting in the LIRA-SAPR software package, as well as with the experimental data of A.I. Sagadatov and calculation according to the current Russian design codes for steel-pipe concrete structures.Result. It has been established that the effective area of operation of columns with a circular cross section is small eccentricities of the longitudinal force.Conclusion. The proposed approach can be applied to the analysis of the stress-strain state and the bearing capacity of pipe-concrete columns of arbitrary section. There are no restrictions on the composition of concrete, and the shell material can be not only steel, but also fiberglass.

A COMPUTATION PERSPECTIVE FOR THE EIGENVALUES OF CIRCULANT MATRICES INVOLVING GEOMETRIC PROGRESSION

In this article, the eigenvalues and inverse of circulant matrices with entries in the first row having the form of a geometric sequence are formulated explicitly in a simple form in one theorem. The method for deriving the formulation of the determinant and inverse is simply using elementary row or column operations. For the eigenvalues, the known formulation of the previous results is simplified by considering the specialty of the sequence and using cyclic group properties of unit circles in the complex plane. Then, the algorithm of eigenvalues formulation is constructed, and it shows as a better computation method.

Evaluation of Technological Parameters of Diabatic Rectification Column Operation with Various Schemes of Coolant Supply to Built-In Reflux Condensers on the Stages

Evaluation of Technological Parameters of Diabatic Rectification Column Operation with Various Schemes of Coolant Supply to Built-In Reflux Condensers on the Stages

DEVELOPMENT OF SOLVENTS ALCOHOL MIXTURE SEPARATION TECHNOLOGY

The paper is devoted to the development of a technology for the regeneration of caprolactam solvents containing n-butanol, amyl alcohol, cyclohexanone, cyclohexanol, as well as isoamyl alcohol and cyclopentanone in impurity amounts. To study the phase equilibrium and the separation process, a computational experiment using AspenPlus V.10.0 was selected. The parameters of the Non Random Two Liquid equation allow reproducing the vapor-liquid equilibrium data and azeotropic properties of the system with a relative error not exceeding 5%. Separation of the mixture by conventional distillation is difficult, which is caused by the presence of three binary azeotropes, as well as three pairs of components characterized by close volatility. The structure of the vapor-liquid equilibrium diagram becomes more complex due to the appearance of new azeotropes with a decrease in pressure. A technological flowsheet for solvent regeneration based on the use of continuous distillation was proposed. The flowsheet contains five columns. At the first stage, preliminary fractionation of the mixture is assumed (the mode of sharp distillation in the first column) with complete separation of cyclohexanone and cyclohexanol in the bottom (vacuum distillation is used to separate this pair) and of a mixture of butanol and amyl alcohol with impurity components in the distillate. Extractive distillation with ethylene glycol was proposed to purify butanol and amyl alcohol from impurities. In the presence of the latter, the volatility of butanol increases in relation to other components. The fourth column is designed for the regeneration of the separating agent. Amyl alcohol separation is provided on the bottom of fifth column. The column operation parameters (the number of stages, the feed stage, the reflux ratio, the ratio of the quantities of the initial mixture and the separating agent) that meet the minimum energy consumption and ensure the production of commercial-quality substances are determined.

Electroblown titanium dioxide and titanium dioxide/silicon dioxide submicron fibers with and without titania nanorod layer for strontium(II) uptake

Nuclear power is a clean alternative to fossil fuels. However, the use of nuclear energy generates hazardous fission products of which 90Sr is the second most important. To remove Sr2+ from aqueous solutions, we synthesized submicron TiO2 and TiO2/SiO2 composite fibers with Ti : Si molar ratios of 3 : 1 (3TiO2–1SiO2) and 1 : 1 (1TiO2–1SiO2) utilizing a novel electroblowing technique. After calcination at 500 °C, the TiO2 and 3TiO2–1SiO2 fibers had a predominantly anatase TiO2 structure with portions of rutile and brookite but the crystallites in the 3TiO2–1SiO2 fibers were smaller due to the SiO2 component. The 1TiO2–1SiO2 fibers were quasi-amorphous. Rutile TiO2 nanorods were grown on the fibers by a hydrothermal method. The rods seemed to grow only on the TiO2 domains of the fiber surface, which affected their size and morphology. In batch adsorption experiments all the fibers had excellent Sr2+ uptake with the hydrothermally modified TiO2 fibers having the highest distribution coefficient (Kd) of 3,490,000 mL g−1. The results show that both anatase and rutile TiO2 can efficiently adsorb Sr2+ from an aqueous environment. Hardly any damage was observed in the nanorods on the TiO2 fibers in a column operation test with flow rates up to 74 mL h−1 which is promising for the use of the fibers in industrial column mode wastewater treatment.

A Preliminary Fault Detection Methodology for Abnormal Distillation Column Operations Using Acoustic Signals

The fault detection of the chemical equipment operation process is an effective means to ensure safe production. In this study, an acoustic signal processing technique and a k-nearest neighbor (k-NN) classification algorithm were combined to identify the running states of the distillation columns. This method can accurately identify various fluid flow states in distillation columns, including normal and flooding states. First, the acoustic signals were collected under normal and abnormal states in an experimental distillation column. Then, the method of dual-domain feature extraction was used to extract the features such as the energy ratio and linear prediction coefficient (LPC). Moreover, the extracted feature parameters were analyzed and compared in a general way. Finally, the k-NN model was used to classify the acoustic signals. The results show that this method had high identification accuracy and provided an important reference for further research.

Selective separation and immobilization process of 137Cs from high-level liquid waste based on silicon-based heteropoly salt and natural minerals

• Silicon-based composite adsorbent was effective for 137 Cs removal. • The interaction mechanism of Cs was studied at the molecular level by density functional theory. • A conceptual process for separation and long-term safe disposal of Cs was proposed. A macro porous silica-based ammonium phosphomolybdate (AMP/SiO 2 ) adsorbent was synthesized and tested for separation and recovery of 137 Cs from real radioactive liquid waste. The excellent adsorption ability and high selectivity of AMP/SiO 2 for 137 Cs were confirmed. AMP/SiO 2 had relatively large decontamination efficiency of 137 Cs exceeding 99% in radioactive wastes, and the decontamination factors of 137 Cs were estimated to be 688 and 270 after adsorption in radioactive waste at 1 and 3 mol/L HNO 3 , respectively. In column operation, the separation and recovery of Cs(I) and coexisting ions could be realized using different eluents, and the recovery rate of Cs(I) was more than 90%. The Cs 3d and Mo 3d X-ray photoelectron spectroscopic spectra of AMP/SiO 2 before and after Cs(I) adsorption, suggesting that the ion exchange process of cesium with crystal lattice cations was the governing mechanism, and cesium ions could spontaneously react with approximately two ammonium ions in each AMP lattice by density functional theory simulation. Further, the crystal binding energy of each revised model showed an upward trend with the progress of the adsorption. After sintering at 1200 °C, CsAlSiO 4 , which could stably solidify eluted cesium, was formed in the allophane-based solidified product. The crystalline properties and volume reduction effect of the sintered products were enhanced with the increase in the allophane content. Ba(II) hardly entered the lattice of CsAlSiO 4 and occupied the Cs(I) site, resulting in minor changes in the crystal structure with substitution of Ba(II) for Cs(I).