Sequential Iteration Method Research Articles

Comprehensive analysis on the economy and energy demand of pressure-swing distillation and pervaporation for separating waste liquid containing multiple components

A large amount of waste liquids containing methanol/acetone/water mixtures are produced in the synthesis of methyl methacrylate (MMA). Under the advocacy of green chemical industry, it is urgent to develop an efficient, economic and energy-saving mixture separation process. Through thermodynamic azeotropic behavior and pressure sensitivity analysis, pressure-swing distillation was determined and the optimal separation pressure of each column in the process was obtained. Due to the composition of waste liquids produced were quite different in MMA production, the pressure-swing distillation separation process was designed to fully achieve the accurate waste liquids treatment. Taking the total annual cost (TAC) as the target, the sequential iteration method was used to optimize the process, and the impact of composition on economy was compared. In order to further realize the energy-saving of the separation process, the pervaporation membrane module was introduced to pretreat the waste liquid in the pressure-swing distillation. The results showed that the TAC of the coupling process was 46% higher than that of the pressure-swing distillation process, and the thermodynamic efficiency was 30% higher. This study provides waste liquid treatment technology for enterprises and analyzes its economic and energy efficiency, which has reference significance for the development of coupled separation technology.

Effect of entrainers with different boiling point sequences on the design and performance for side-stream extractive distillation processes

BackgroundAn azeotropic mixture of acetone and n-heptane is commonly found in many pharmaceutical wastewaters. In this work, the separation of acetone / n-heptane was studied using intermediate- and high-boiling-point entrainers (benzene and p-xylene, respectively). MethodsTo maximize the economic benefits and mitigate the economic and environmental impact of the separation process, traditional extractive distillation and side-stream extractive distillation processes were developed for different entrainers. The sequential iteration method was employed to optimize the extractive distillation process, with the total annual cost as the constraint objective. Significant findingsThe results show that p-xylene can facilitate the separation of acetone / n-heptane, with high efficiency and low energy consumption, when using a double distillation column. Among the four separation processes developed, the p-xylene side-stream extractive distillation process delivers the best economic and environmental performance, with a total annual cost of 6.04 × 105 $/y and CO2 emissions of 1114.66 kg/y. Compared to the case of traditional p-xylene extractive distillation and benzene side-stream extractive distillation processes, the total annual cost of the p-xylene side-stream extractive distillation process was reduced by 9.56% and 49.22%, respectively, while the corresponding CO2 emissions were reduced by 15.71% and 48.85%.

Stability analysis of surrounding rock of high-pressure cavern tunnel under coupled stress-damage-seepage

The high-pressure cavern is located below the diversion tunnel, which will produce a large seepage force during the excavation process. Consider the effect of seepage field on the stress field with the seepage force, consider the effect of stress and damage on the seepage field through the improved Louis formula, and establish the stress-damage-permeability coefficient equation to consider the effect of stress and damage on the seepage field. The three-dimensional elastoplastic damage finite element analysis of rock mass structure has established a stress-damage-seepage calculation model for surrounding rock excavation of a diversion tunnel with high-pressure cavities. A sequential iteration method is proposed to summarize the above factors and then iteratively solve them in a certain order. Based on a water diversion project, the relevant calculation examples are appropriately simplified. The results show that the seepage effect has a greater impact on the stability of the surrounding rock of the diversion tunnel, and it can be seen that the coupling effect cannot be ignored in the analysis of the stability of the surrounding rock of the excavation of the diversion tunnel.

Quantum chemistry of solvent selectivity and economic, exergy and environment analysis of extractive distillation process for separating binary azeotropic mixture

BackgroundAfter ammoniation of propacetamol hydrochloride, the liquor contains an azeotropic mixture of acetone and diethylamine. The mixture must be separated to reuse the solvent and the raw material. However, the separation of acetone and diethylamine is difficult because the boiling point difference is only 0.6°C. MethodsIn this study, the mechanism of separating azeotropes was studied by quantum chemical calculations of the σ-profiles, interaction energy and molecular conformation. The vapor-liquid equilibrium data were supplemented by experimental analysis of the vapor-liquid equilibrium for cyclohexanol and diethylamine. The relative volatility of the light and heavy components of the azeotrope was investigated after adding the solvent. Sequential iteration method was used to optimize the extractive distillation process. The parameters in process such as the feeding position, number of stages and the amount of solvent are optimized, and the minimum total annual cost is obtained. Significant findingsThe results showed that the two-column feed preheating extractive distillation process was the lowest. The results showed that the two-column feed preheating extractive distillation process afforded the lowest total annual cost. Thermodynamic and environmental analyses showed that the two-column feed preheating extractive distillation process afforded good energy-saving, with minimal environmental impact. This study is significant for implementing the extractive distillation process for azeotrope separation and the sustainable development of acetone and diethylamine products.

Relativistic Dirac analyses of proton scattering from $$^{92}{\text {Zr}}$$

Relativistic coupled channel analyses based on the Dirac equation are presented for polarized 800-MeV proton inelastic scatterings from an axially symmetric deformed nucleus $$^{92}{\text {Zr}}$$ by using an optical potential model and the first-order collective model. The sequential iteration method using a computer program is employed to solve the complicated Dirac coupled channel equations. The optical potential parameters of the Woods–Saxon shape and the deformation parameters of several low-lying excited states are determined phenomenologically and analyzed. The coupled channel effect between the excited states that belong to the ground-state rotational band is investigated.

Insight into separation of azeotrope in wastewater to achieve cleaner production by extractive distillation and pressure-swing distillation based on phase equilibrium

There are a large number of azeotropes in the binary system of alkanes and alcohols in the industrial wastewater from the reaction of vanadium pentoxide with alkanes to produce alkylvanadate. In order to protect the environment, utilize resources and clean production, the extractive distillation process with high boiling solvent as extractant is usually used to separate the azeotropes in industrial products. However, some intermediate-boiling solvents compared with the two key components to be separated are used as extractant in extractive distillation. In this work, the binary azeotropic system of n-heptane and isoamyl alcohol in wastewater was separated by extractive distillation with intermediate-boiling solvents, pressure-swing distillation and pressure-swing distillation with thermal integration. The binary interaction parameters of isoamyl alcohol and butyl acetate were obtained by correlating and regressing the experimental data of vapor-liquid equilibrium at atmospheric pressure. Taking total annual cost minimum as the objective function, the optimal design parameters of the three processes were obtained by sequential iteration method. Compared with the extractive distillation and pressure-swing distillation, pressure-swing distillation with thermal integration can save the cost up to 29.38%, increase the thermodynamic efficiency up to 445.39%, reduce the global warming potential up to 39.34% and the decrease the acidification potential up to 39.34%. This work provides an effective reference for better separation of azeotropes and wastewater treatment.

A two-dimensional transient fluid-thermal coupling method for temperature rising calculation of transformer winding based on finite element method

In order to study the characteristics of the temperature variation in oil-immersed power transformer windings during operation, a two-dimensional transient fluid-thermal coupling calculation method for the transient temperature rising of transformer windings is proposed. Based on the dimensionless least-square finite element method (DLSFEM), the two-dimensional transient fluid-thermal coupling calculation method calculates the velocity distribution of the transformer flow field at different time instants, and based on the upwind finite element method, the temperature distribution at each moment is calculated. Considering the influence of the nonlinear material properties and winding Joule loss on the calculation results, the sequential iteration method is applied to solve the fluid-thermal coupling problem, and finally, the characteristics of the field temperature change are obtained. Compared with the traditional least-square finite element method, the DLSFEM has smaller stiffness matrix number conditions, and the corresponding discrete equations have better convergence. An oil-immersed power transformer winding model is taken as an instance, and the temperature distribution is calculated by the proposed method and the commercial computational fluid dynamic software Fluent. The calculation results of the proposed method are basically consistent with those of Fluent, and its iterative number is much less than that of Fluent, which greatly improves the calculation efficiency.

Application of green solvent to separate the minimum boiling point azeotrope based on molecular structure prediction and experimental verification

With the increasing market demand of methyl isobutyl ketone, the by-product waste liquid produced in the production process is more and more harmful to the environment. In order to reduce pollution and make full use of resources, the azeotrope of 1-butanol and methyl isobutyl ketone must be recycled. In this paper, the vapor-liquid equilibrium data were obtained by experiments, and the binary interaction parameters were obtained by regression. Through the analysis of relative volatility, σ-profiles and structure conformation could select suitable extractant. The main operating parameters of extractive distillation process were optimized by sequential iteration method. The recovered purity of 1-butanol and methyl isobutyl ketone were 99.98 mol% and 99.98 mol%, respectively, which can be used sustainably. From the three aspects of economy, energy and environmental pollution, the process of using parameters obtained from experimental data and the process of using predicted parameters were analyzed and compared. The total annual cost of the process with the parameters obtained from the experiment is 2.5% less than that with the predicted parameters, the thermal efficiency is increased by 3.38%, and the carbon emission is reduced by 2.96%. Therefore, using real interaction parameters plays an important role in engineering simulation and industrialization.

Numerical and Experimental Investigation of Temperature Distribution for Oil-Immersed Transformer Winding Based on Dimensionless Least-Squares and Upwind Finite Element Method

To accurately analyze the temperature rising and locate the hot-spot of oil-immersed transformer windings, a hybrid method based on the dimensionless least-squares finite element method (DLSFEM) and upwind finite element method (UFEM) is proposed in this paper. To solve the fluid-thermal coupling problem, the sequential iteration method was utilized. After that, the two-side equilibration method and the Jacobi preconditioned conjugate gradient method were used to solve the equations. Moreover, a product-level experimental platform for oil-immersed transformer windings was built. The influence of the turn-to-turn insulation and gravity on the temperature was discussed, and the results show that the influence is significant. To verify the effectiveness of the proposed method, a comparison between the simulation results of the proposed method and experimental results were made, which shows a good agreement. Aiming at verifying the efficiency of the proposed method, the convergence of the proposed method was compared with that of the commercial computational fluid dynamic (CFD) software Fluent. The results indicate that the convergence speed of the proposed method is much faster than that of Fluent, which means a better performance of the new method.

Dirac phenomenological analyses for the proton scatterings from nickel isotopes

Relativistic Dirac coupled channel analyses are performed phenomenologically using an optical potential model for the intermediate energy proton inelastic scatterings from nickel isotopes, 58Ni and 60Ni. The first-order rotational collective model is used for the transition optical potentials to describe the low-lying excited collective states of the ground state rotational band. The complicated Dirac coupled channel equations are solved phenomenologically by varying the optical potential and the deformation parameters to reproduce the experimental data, using a computer program that uses a sequential iteration method. The channel-coupling effects of the multistep transition process for the excited states of the ground state rotational band are found to be strong and lead the calculation results to better agreement with the experimental data when the channel coupling between the excited states is added in the calculation. The Dirac equations are reduced to the second-order differential equations to obtain the Schrödinger equivalent effective central and spin–orbit optical potentials, and the obtained effective potentials are analyzed.

Dirac coupled-channel analyses of the high-lying excited states at 22Ne(p,p′)22Ne

Dirac phenomenological coupled channel analyses are performed using an optical potential model for the high-lying excited vibrational states at 800 MeV unpolarized proton inelastic scatterings from $^{22}$Ne nucleus. Lorentz-covariant scalar and time-like vector potentials are used as direct optical potentials and the first-order vibrational collective model is used for the transition optical potentials to describe the high-lying excited vibrational collective states. The complicated Dirac coupled channel equations are solved phenomenologically using a sequential iteration method by varying the optical potential and the deformation parameters. Relativistic Dirac coupled channel calculations are able to describe the high-lying excited states of the vibrational bands in $^{22}$Ne clearly better than the nonrelativistic coupled channel calculations. The channel-coupling effects of the multistep process for the excited states of the vibrational bands are investigated. The deformation parameters obtained from the Dirac phenomenological calculations for the high-lying vibrational excited states in $^{22}$Ne are found to agree well with those obtained from the nonrelativistic calculations using the same Woods-Saxon potential shape.

Dirac coupled channel analyses of proton inelastic scattering from the 40Ar nucleus

0.8 GeV proton inelastic scatterings from $^{40}$Ar nucleus are analyzed using an optical potential model in the Dirac coupled channel formalism. A rotational collective model is used to obtain the transition optical potentials for the low lying excited states of the rotational band. The optical potential parameters of a Woods-Saxon shape and the deformation parameters of the excited states are searched phenomenologically to reproduce the experimental differential cross-section data by using the sequential iteration method. The effect of a multistep process is investigated by including the channel coupling between two excited states in addition to the couplings between the ground state and the excited states. The calculated deformation parameters of the excited states are compared with those obtained by using the nonrelativistic calculations. The results of the Dirac coupled channel calculations are found to show pretty good agreements with the experimental data of the ground state and the low-lying excited states. The multistep excitation process via the channel coupling with the second $2^+$ state is found to be important for the excitation of the $4^+$ state at the inelastic scatterings from the deformed nucleus, $^{40}$Ar.

Dirac phenomenological analyses of unpolarized proton inelastic scattering from 22Ne

Unpolarized 800 MeV proton inelastic scatterings from an s-d shell nucleus $^{22}$Ne are analyzed using phenomenological optical potentials in the Dirac coupled channel formalism. The first-order rotational collective model is used to obtain the transition optical potentials for the low lying excited collective states that belong to the ground state rotational band of the nucleus. The optical potential parameters of Woods-Saxon shape and the deformation parameters of the excited states are varied phenomenologically using the sequential iteration method to reproduce the experimental differential cross section data. The effective central and spin-orbit optical potentials are obtained by reducing the Dirac equations to the Schr\"odinger-like second-order differential equations and the surface-peaked phenomena are observed at the real effective central potentials when the scattering from $^{22}$Ne is considered. The obtained deformation parameters of the excited states are compared with those of the nonrelativistic calculations and another s-d shell nucleus $^{20}$Ne. The deformation parameters for the $2^+$ and the $4^+$ states of the ground state rotational band at the nucleus $^{22}$Ne are found to be smaller than those of $^{20}$Ne, indicating that the couplings of those states to the ground state are weaker at the nucleus $^{22}$Ne compared to those at the nucleus $^{20}$Ne. The multistep channel coupling effect is confirmed to be important for the $4^+$ state excitation of the ground state rotational band at the proton inelastic scattering from the s-d shell nucleus $^{22}$Ne.

Water-rock interaction and reactive-transport modeling using elemental mass-balance approach: I. The methodology

Water-rock interaction and reactive transport modeling is an important tool for deciphering chemical and physical reactions occurring in sediments and rocks. The modeling methodology calls for solving conservation equations to account for the interaction between mass-transfer and reaction processes using a sequential iteration numerical method. The formalism presented here improves upon the traditional approach by reformulating conservation equations to express chemical elemental mass evolution. The elemental conservation equations describe mass change through mass-transfer and kinetic reactions of solids, and solute-solute interaction (equilibrium) reaction expressions. The system of equations is solved using a sequential iteration method, whereby globally discretized mass-transfer coefficients of conservation equations are injected explicitly into the conservation equations and solved locally at each node. The result is a mathematically simple approach that eliminates the traditionally required use of primary and secondary species classification. The formalism also allows the use of solute-specific diffusivities. In addition, the tight coupling between mass-transfer and reactions achieved by the methodology also allows nonlinear self-organization or pattern-forming phenomena to be captured. The methodology is demonstrated with simulations of (1) a diffusive-reaction system involving patterned hematite nucleation, and (2) a flow-through system where CO2-charged water interacts with formation water in a sandstone reservoir. Both are isothermal one-dimensional simulations. In the first example, convergent diffusive infiltration of Fe++ and O2 from two opposite ends produces patterned precipitates. A natural analog of such phenomena is the occurrence of iron-oxide concretions in Navajo Sandstones of Utah and Arizona. The second example demonstrates the formation of a diffusive solute migration front ahead of advective effluent displacement and reaction fronts. Such phenomena are observed when large quantities of CO2 are injected into geologic formations. The early arrival of diffusive solute fronts at nearby monitoring wells are noted by decreasing water pH and raised alkalinity some time before the arrival of the effluent.

SYSTEMATIC DIRAC ANALYSES OF PROTON INELASTIC SCATTERINGS FROM AXIALLY SYMMETRIC DEFORMED NUCLEI

Relativistic Dirac coupled channel analyses using optical potential model are performed for the 800 MeV proton inelastic scatterings from 26 Mg and the results are compared with those from several other axially symmetric deformed nuclei for the systematic Dirac analyses. Employing scalar-vector model, scalar and time-like vector optical potentials in Lorentz covariant form are calculated phenomenologically by solving Dirac coupled channel equations using sequential iteration method. Dirac equations are reduced to second-order differential equations to obtain Schrödinger equivalent effective central and spin-orbit optical potentials and it is found that the heavier deformed nucleus has the larger effective central potential strength. Using the first-order rotational collective model to describe the low-lying excited states of ground state rotational band in the deformed nuclei, deformation parameters for the excited states are calculated and it is observed that the lighter deformed nucleus has the larger deformation parameter for the lowest lying excited 2+ state at the 800 MeV proton inelastic scattering, indicating the stronger coupling to the ground state compared to that of heavier nucleus.

Relativistic Analysis of Intermediate Energy Proton Inelastic Scatterings from Heavy Deformed Nuclei

A relativistic coupled channel analysis based on the Dirac equation is performed for inelastic scattering of an intermediate energy proton from a heavy, deformed nucleus by using an optical potential model. In order to describe the low-lying excited states of the deformed nucleus, we used a rotational collective model to get the transition optical potentials. The Dirac coupled-channel equations are solved numerically to calculate the di erential cross sections by using the sequential iteration method. Employing Dirac phenomenology, we vary the optical potential parameters and deformation parameters to reproduce the experimental observables. The theoretical results are observed to agree reasonably well with the inelastic scattering experimental data of 800 MeV p+176Yb, and the importance of the multistep process for inelastic scatterings at a deformed nucleus is con rmed. The e ective Schr odinger-equivalent central and spin-orbit potentials are calculated by reducing the Dirac equation to a Schr odinger-like second-order di erential equation and by comparison them with those of a Schr odinger calculation in which the spin-orbit potential is not included, showing the relatively large strength of a real central potential. Surface-peaked phenomena are not observed for e ective central potentials when the heavy, deformed nucleus of 176Yb is considered.

Numerical verification of solutions for Signorini problems using Newton‐like method

AbstractWe proposed a numerical method to verify the existence of solutions for a simplified Signorini problem (Comput. Math. Appl. 2000; 40:1003–1013). Using sequential iteration method, we numerically constructed a set containing solutions that satisfies the hypothesis of Schauder's fixed point theorem in a certain Sobolev space. It is difficult to apply this method to the problem of which associated operator is not retractive in a neighborhood of the solution. In this paper, in order to overcome such a difficulty, we describe an alternative approach to this problem. Numerical examples are presented. Copyright © 2007 John Wiley & Sons, Ltd.

既抽出データを削除しないファジィハフ変換

In conventional fuzzy Hough transforms, lines are detected using a sequential iteration method that deletes data points on the detected lines. Detecting another line intersecting the detected lines is difficullt because some data points have been deleted in the previous process. We propose a fuzzy Hough transform method that preserves all the data in the iterative detection process. In addition, parameters of lines are refined so that the lines fit the data point pattern better than by using the conventional sequential iteration method.