An optimization method for enhancement of gas–liquid mass transfer in a bubble column reactor based on the entropy generation extremum principle

In this study,an optimization method is proposed to enhance the gas–liquid mass transfer in bubble column reactor based on the entropy generation extremum principle.The mass transfer–induced entropy generation can be maximized with the increase of mass transfer rate,based on which the velocity field can be optimized.The oxygen gas–liquid mass transfer is the major rate–limiting step of the toluene emissions biodegradation process in bubble column reactor,so the entropy generation due to oxygen mass transfer is used as the objective function,and the conservation equations of the gas–liquid flow and species concentration are taken as constraints.This optimization problem is solved by the calculus of variations,the optimal liquid flow pattern is obtained and the relationship of the maximum mass transfer enhancement on viscous dissipation is revealed,which can be used to improve the design of internal structure of the bubble column reactor.

Reliability-based life-cycle cost seismic design optimization of coastal bridge piers with nonuniform corrosion using different materials

Reinforcement corrosion is the main cause of performance deterioration of reinforced concrete(RC)structures.Limited research has been performed to investigate the life-cycle cost(LCC)of coastal bridge piers with nonuniform corrosion using different materials.In this study,a reliability-based design optimization(RBDO)procedure is improved for the design of coastal bridge piers using six groups of commonly used materials,i.e.,normal performance concrete(NPC)with black steel(BS)rebar,high strength steel(HSS)rebar,epoxy coated(EC)rebar,and stainless steel(SS)rebar(named NPC-BS,NPC-HSS,NPC-EC,and NPC-SS,respectively),NPC with BS with silane soakage on the pier surface(named NPC-Silane),and high-performance concrete(HPC)with BS rebar(named HPC-BS).First,the RBDO procedure is improved for the design optimization of coastal bridge piers,and a bridge is selected to illustrate the procedure.Then,reliability analysis of the pier designed with each group of materials is carried out to obtain the time-dependent reliability in terms of the ultimate and serviceability performances.Next,the repair time of the pier is predicted based on the time-dependent reliability indices.Finally,the time-dependent LCCs for the pier are obtained for the selection of the optimal design.

Modeling and optimization of industrial Fischer–Tropsch synthesis with the slurry bubble column reactor and iron-based catalyst

To optimize industrial Fischer-Tropsch （IT） synthesis with the slurry bubble column reactor （SBCR） and iron- based catalyst, a comprehensive process model for IT synthesis that includes a detailed SBCR model, gas liquid separation model, simplified CO2 removal model and tail gas cycle model was developed. An effective iteration algorithm was proposed to solve this process model, and the model was validated by industrial demonstration experiments data （SBCR with 5.8 m diameter and 30 m height）, with a maximum relative error 〈 10% for predicting the SBCR performances. Subsequently, the proposed model was adopted to optimize the industrial SBCR performances simultaneously considering process and reactor parameters variations. The results show that C5＋yield increases as catalyst loading increases within 10-70 ton and syngas H2/CO value decreases within 1.3-1.6, but it doesn＇t increase obviously when the catalyst loading exceeds 45 ton （about 15 wt% concentration）. Higher catalyst loading will result in higher difficulty for wax/catalyst separation and higher catalyst cost. There- fore, the catalyst loading （45 ton） is recommended for the industrial demonstration SBCR operation at syngas H2/ CO = 1.3, and the C5 ＋ yield is about 402 ton＂ per day, which has an about 16% increase than the industrial dem- onstration run result.

Optimization of the reflux ratio of benzene-toluene stage distillation columns by the Cuckoo algorithm

In this study, an enthalpy-concentration method was applied in order to model a steady state continuous benzene-toluene mixture distillation column. For a distillation tower such as the benzene- toluene splitter, there are relatively few degrees of freedom that can be manipulated in order to minimize the total annualized cost. The reflux ratio can influence the steady-state operating point and therefore influence the total annualized cost. The trade-offs between reflux ratios and total annualized cost were discussed. The Cuckoo optimization algorithm was applied to obtain a correlation for the optimum value of the reflux ratio as a power function of the economic parameters of energy price and capital cost. The results show that, at low energy price or high capital cost, the optimum reflux factor is high.

Mechanical performance study of the retractable pier column after stiffening

To solve the problem that the overlapping parts of a retractable pier column are prone to damage,this paper proposed the reinforcing measure of setting a stiffener ring at the bottom of the steel pipe.To study how the stiffener-ring parameters influence the mechanical properties of the pier column.12 scale model specimens(including nine specimens with stiffener-ring widths of 40,50,and 60 mm and three unstiffened comparison specimens)were tested under axial compression.Based on the test results,the specimen load-displacement,load-deflection,and load-strain curves were analyzed,and a finite-element model of a pier column under axial compression was established to determine the optimal stiffener size.The results show that setting a stiffener ring enhances the cooperative working ability between the steel pipe and the internal filling material and restrains the lateral deformation of the pier column,thereby improving the ultimate bearing capacity and overall stability of the pier column.The ultimate bearing capacity of the pier column is related to the width and thickness of the stiffener ring.The optimal size of the stiffener ring of the model pier column is 70 mm in width and 4 mm in thickness.The present research results provide a reference for designing compressible pier columns and column stiffening in mines and have important practical significance.

Investigations into Optimization Models of Crude Oil Distillation Column in the Context of Feed Stock and Market Value

This paper proposes optimization models of crude oil distillation column for both limited and unlimited feed stock and market value of known products prices. The feed to the crude distillation column was assumed to be crude oil containing naphtha gas, kerosene, petrol and diesel as the light-light key, light key, heavy key and heavy-heavy key respectively. The models determined maximum concentrations of heavy key in the distillate and light key in the bottom for limited feed stock and market condition. Both were impurities in their respective positions of the column. The limiting constraints were sales specification concentration of light key in the distillate [ ], heavy key in the bottom [ ] and an operating loading constraint of flooding above the feed tray. For unlimited feed stock and market condition, the optimization models determined the optimum separation [ and ] and feed flow rate that would give maximum profit with minimum purity sales specification constraints of light key in the distillate and heavy key in the bottom as stated above. The feed loading was limited by the reboiler capacity. However, there is need to simulate the optimization models for an existing crude oil distillation column of a refinery in order to validate the models.

Hysteretic behavior of post-tensioned precast segmental CFT double-column piers

Considering the desirable behavior of concrete filled steel tube(CFT)columns and the complicated behavior of segmental double-column piers under cyclic loads,three post-tensioned precast segmental CFT double-column pier specimens were tested to extend their application in moderate and high seismicity areas.The effects of the number of CFT segments and the steel endplates as energy dissipaters on the seismic behavior of the piers were evaluated.The experimental results show that the segmental piers exhibited stable hysteretic behavior with small residual displacements under cyclic loads.All the tested specimens achieved a drift ratio no less than 13%without significant damage and strength deterioration due to the desirable behavior of CFT columns.Since the deformation of segmental columns was mainly concentrated at the column-footing interfaces,the increase of the segment numbers for each column had no obvious effects on the loading capacity but reduced the initial stiffness of the specimens.The use of steel endplates improved the bearing capacity,stiffness and energy dissipation of segmental piers,but weakened their self-centering capacity.Fiber models were also proposed to simulate the hysteretic behavior of the tested specimens,and the influences of segment numbers and prestress levels on seismic behavior were further studied.

Aperture shape optimization in intensity-modulated radiation therapy planning

The gradient element of the aperture gradient map is utilized directly to generate the aperture shape without modulation.This process can be likened to choosing the direction of negative gradient descent for the generic aperture shape optimiza-tion.The negative gradient descent direction is more suitable under local conditions and has a slow convergence rate.To overcome these limitations,this study introduced conjugate gradients into aperture shape optimization based on gradient modulation.First,the aperture gradient map of the current beam was obtained for the proposed aperture shape optimiza-tion method,and the gradients of the aperture gradient map were modulated using conjugate gradients to form a modulated gradient map.The aperture shape was generated based on the modulated gradient map.The proposed optimization method does not change the optimal solution of the original optimization problem,but changes the iterative search direction when generating the aperture shape.The performance of the proposed method was verified using cases of head and neck cancer,and prostate cancer.The optimization results indicate that the proposed optimization method better protects the organs at risk and rapidly reduces the objective function value by ensuring a similar dose distribution to the planning target volume.Compared to the contrasting methods,the normal tissue complication probability obtained by the proposed optimization method decreased by up to 4.61%,and the optimization time of the proposed method decreased by 5.26%on average for ten cancer cases.The effectiveness and acceleration of the proposed method were verified through comparative experiments.According to the comparative experiments,the results indicate that the proposed optimization method is more suitable for clinical applications.It is feasible for the aperture shape optimization involving the proposed method.

An Optimization Model for the Production Planning of Overall Refinery

This article addresses a production planning optimization problem of overall refinery. The authors formulated the optimization problem as mixed integer linear programming. The model considers the main factors for optimizing the production plan of overall refinery related to the use of run-modes of processing units. The aim of this planning is to decide which run-mode to use in each processing unit in each period of a given horizon, to satisfy the demand, such as the total cost of production and inventory is minimized. The resulting model can be regarded as a generalized lot-sizing problem where a run-mode can produce and consume more than one product. The resulting optimization problem is large-sized and NP-hard. The authors have proposed a column generation-based algorithm called branch-and-price （BP） for solving the interested optimization problem. The model and implementation of the algorithm are described in detail in this article. The computational results verify the effectiveness of the proposed model and the solution method.

Systematic exploration of the applicability of the idiomatic vapor balance rule to distillation column consolidation

For N-component distillation(N≥3),consolidation between different column sections is an inevitable manipulation when synthesizing complex distillation configurations.In the consolidation,the idiomatic vapor balance(IVB)rule,in which the larger vapor flowrate in the two columns before consolidation will be chosen as the balanced vapor flowrate at the consolidation point,has been widely used.However,the applicability of the IVB rule has not been verified,which is of essential importance to the accuracy of the distillation configuration synthesis.In the present study,the applicability of the IVB rule to distillation column consolidation was systematically explored by rigorous method for the first time.First,the separation of ideal and non-ideal three-component mixtures with variable compositions was studied,and the optimized configurations before and after consolidation were determined by a rigorous method.The results indicated that for the separation of an ideal mixture,the IVB rule was applicable for the whole composition range,while for the separation of a non-ideal mixture,the IVB rule was only applicable for very limited composition range.Finally,two cases of synthesizing distillation configurations for the separation of non-ideal mixtures were studied to verify the remarkable deviations the IVB rule may cause.The results indicated that the applicability of the shortcut method using the IVB rule to the distillation configuration synthesis depended on the composition of the non-ideal mixture,and a remarkable error might result and the truly optimal configuration might be missed if the IVB rule is applied to a non-ideal mixture.

Simulation research on the energy dissipation and shock absorption performance of a swing column device based on fuzzy control

Double-column bridge piers are prone to local damage during earthquakes,leading to the destruction of bridges.To improve the earthquake resistance of double-column bridge piers,a novel swing column device(SCD),consisting of a magnetorheological(MR)damper,a current controller,and a swing column,was designed for the present work.To verify the seismic energy dissipation ability of the SCD,a lumped mass model for a double-column bridge pier with the SCD was established according to the low-order modeling method proposed by Steo.Furthermore,the motion equation of the double-column bridge pier with the SCD was established based on the D′Alembert principle and solved with the use of computational programming.It was found that the displacement response of the double-column bridge pier was effectively controlled by the SCD.However,due to rough current selection and a time delay,there is a significant overshoot of the bridge acceleration using SCD.Hence,to solve the overshoot phenomenon,a current controller was designed based on fuzzy logic theory.It was found that the SCD design based on fuzzy control provided an ideal shock absorption effect,while reducing the displacement and acceleration of the bridge pier by 36.43%‒40.63%and 30.06%‒33.6%,respectively.

Crushing analysis and multi-objective optimization of bitubular hexagonal columns with ribs

In order to improve the crashworthiness of thin-walled columns, the energy absorption characteristics of three columns under quasi-static axial crushing loads were analyzed through LS-DYNA. Numerical results show that the energy absorption capability of the bitubular hexagonal columns with middle to middle(MTM) ribs is the best, followed by the bitubular hexagonal columns with corner to corner(CTC) ribs and the bitubular hexagonal columns without(NOT) ribs, respectively. Then, the MTM rib was optimized by using multi-objective particle swarm optimization algorithm. Through the analysis of the Pareto front for specific energy absorption(SEA, A_(se)) and peak crushing force(PCF, F_(pc)), it is found that there is a vertex on the Pareto front. The vertex has the design parameters of t_1=1.2 mm, t_2=1.2 mm, A_(se)=11.3729 k J/kg, F_(pc)=235.8491 kN. When the PCF is in a certain size, on the left of the vertex, the point with t_2=1.2 mm has the biggest SEA, meanwhile on the right of the vertex, the point with t_1=1.2 mm has the biggest SEA. Finally, the global sensitivity analysis was conducted to investigate the effect of two design parameters. The result is obtained that both SEA and PCF for MTM are more sensitive to t_1 rather than t_2 in the design domain.

Simulation Optimization and Experimental Study of Cross-Wall Adiabatic Dividing Wall Column Used to Separate Hexane-Heptane-Octane System

Through separation of the hexane-heptane–octane system in a cross-wall adiabatic dividing wall column, the effects of feed position, side-draw position, liquid split ratio, vapor split ratio and their interactions on the energy consumption were analyzed by Aspen Plus under the constant product purity, and the response surface model for the energy consumption was regressed. Based on the restriction on the optimal operating zone, the comparison of different combinations of surrogate models and optimization methods showed that, the combination of the Kriging model and multi-island genetic algorithm(Kriging-MIGA) had better prediction ability than the combination of the response surface model and partial derivative method(RSM-PD), and RSM-PD had better optimization effect than Kriging-MIGA. With a self-made cross-wall adiabatic dividing wall column, the temperature at measuring points and the energy consumption were measured during experiments, the comparison between measured values and simulated ones demonstrated that the optimized values of variables searched by RSM-PD and Kriging-MIGA could be both used as the optimum technological conditions since the experimental reliability was ensured, with the optimum technological conditions shown below: The feed position is 6, the side-draw position is 7, the combinations of liquid split ratio and vapor split ratio are [0.14, 0.5] and [0.16, 0.52], respectively. RSM-PD and Kriging-MIGA can provide the appropriate optimization methods for the dividing wall column.

Enhancing recovery of uranium column bioleaching by process optimization and kinetic modeling

This research aimed to enhance the column bioleaching recovery of uranium ore by Acidithiobacillus ferrooxidans.Seven factors were examined for their significance on bioleaching using a Plackett-Burman factorial design.Four significant variables([Fe2+]initial,pH,aeration rate and inoculation percent)were selected for the optimization studies.The effect of these variables on uranium bioleaching was studied using a central composite design(CCD).The optimal values of the variables for the maximum uranium bioleaching recovery(90.27±0.98)%were as follows:[Fe2+]initial=2.89g/L,aeration rate420mL/min,pH1.45and inoculation6%(v/v).[Fe2+]initial was found to be the most effective parameter.The maximum uranium recovery from the predicted models was92.01%.This value was in agreement with the actual experimental value.The analysis of bioleaching residue of uranium ore under optimum conditions confirmed the formation of K-jarosite on the surface of minerals.By using optimal conditions,uranium bioleaching recovery is increased at column and jarosite precipitation is minimized.The kinetic model showed that uranium recovery has a direct relation with ferric ion concentration.

A dynamic control structure of liquid-only transfer stream distillation column

The intention of this fundamental work is to explore the manipulation of a mixture of benzene,toluene and o-xylene separated from liquid-only transfer divided-wall column(LTS-DWC).First,two control structures are clearly proposed,including seven component control loops(CS1)and seven temperature control loops(CS2).However,two control structures can handle ±10% feed disturbances rather than larger feed disturbances.Subsequently,an equivalent four-column model by introducing withdraw ratio is developed to discuss the effect of two liquid-only side-stream on the overall reboiler duty.It is indicated that the second liquid-only side-stream withdraw ratio strongly affects the overall energy consumption.Hence,six-component control loops within the fixed second liquid-only side-stream withdraw ratio(CS3)is proposed and the purity of products returns to set value even as facing ±20% feed disturbances.Finally,based on the above results,it is established a temperature control structure(CS4)for controlling fixed second liquid-only side-stream withdraw ratio,which can cope with ±15% disturbances.Inspired by these findings,an insight into the dynamic control of LTS-DWC promotes the industrial implementation of DWC through new liquid-only side-stream configurations.

Mathematical modeling of a slurry reactor for DME direct synthesis from syngas

In this paper,an axial dispersion mathematical model is developed to simulate a three-phase slurry bubble column reactor for direct synthesis of dimethyl ether（DME） from syngas.This large-scale reactor is modeled using mass and energy balances,catalyst sedimentation andsingle-bubble as well as two-bubbles class flow hydrodynamics.A comparison between the two hydrodynamic models through pilot plantexperimental data from the literature shows that heterogeneous two-bubbles flow model is in better agreement with the experimental data thanhomogeneous single-bubble gas flow model.Also,by investigating the heterogeneous gas flow and axial dispersion model for small bubblesas well as the large bubbles and slurry（i.e.including paraffins and the catalyst） phase,the temperature profile along the reactor is obtained.Acomparison between isothermal and non-isothermal reactors reveals no obvious performance difference between them.The optimum values ofreactor diameter and height were obtained at 7 m and 50 m,respectively.The effects of operating variables on the axial catalyst distribution,DME productivity and CO conversion are also investigated in this research.

Active set truncated-Newton algorithm for simultaneous optimization of distillation column

An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.

A Multi-Agent Immune Network Algorithm and Its Application to Murphree Efficiency Determination for the Distillation Column

Artificial Immune Network （aiNet） algorithms have become popular for global optimization in many modem industrial applications. However, high-dimensional systems using such models suffer from a potential premature convergence problem. In the existing aiNet algorithms, the premature convergence problem can be avoided by implementing various clonal selection methods, such as immune suppression and mutation approaches, both for single population and multi-population cases. This paper presents a new Multi-Agent Artificial Immune Network （Ma-aiNet） algorithm, which combines immune mechanics and multiagent technology, to overcome the premature convergence problem in high-dimensional systems and to efficiently use the agent ability of sensing and acting on the environment. Ma-aiNet integrates global and local search algorithms. The perform- ance of the proposed method is evaluated using 10 benchmark problems, and the results are compared with other well-known intelligent algorithms. The study demonstrates that Ma-aiNet outperforms other algorithms tested. Ma-aiNet is also used to determine the Murphree efficiency of a distillation column with satisfactory results.

MPC of distillation column with side reactors for methyl acetate

This paper focuses on the dynamic control of distillation column with side reactors(SRC) for methyl acetate production. To obtain the optimum integrated structure and steady state simulation, the systematic design approach based on the concept of independent reaction amount is applied to the process of SRC for methyl acetate production. In addition to the basic control loops, multi-variable model predictive control modular with methyl acetate concentration and temperature of sensitive plate is designed. Then, based on process simulation software Aspen Plus, dynamic simulation of SRC for methyl acetate production is used to verify the effectiveness of the control scheme.

Liquid Flow Distribution in a New Type of Multi-tube Column

A new type of multi-tube column, in which a novel internal-structure is installed in the bed of random packing, has been invented. The internal-structure reduces the hydraulic radius of the column and adjusts the gas/liquid flow so that the liquid maldistribution is greatly abated. A mathematical model with boundary conditions based on close-open mechanism at the internal-structure was established to study the hydraulic behavior of such a column and experiments were carded out to verify the applicability of the model. Predictions from the model agreed well with experimental results. The optimal ratio of the hydraulic diameter of the new multi-tube column to the packing element diameter is found to be 17.5 to 23.3 by employing the optimization method of nonlinear programming. And this new type of multi-tube column opens a new way for random packing columns to be scaled up for industry.