Mathematical Model of the Liquid Membrane Extractive Column. Sensitivity to Operating Parameters

2008 ◽  
Vol 59 (3) ◽  
pp. 336-345
Author(s):  
Daniel Dinculescu ◽  
Vasile Lavric
Keyword(s):  
Mathematical Model ◽  
Aqueous Phase ◽  
Closed Loop ◽  
Liquid Membrane ◽  
Extraction Column ◽  
Model Parameters ◽  
Operating Parameters ◽  
Back Extraction ◽  
Orthogonal Collocation ◽  
Transfer Coefficients

The extraction-back extraction column of low concentration species by means of an organic closed loop flow, considered as liquid membrane, was modelled then simulated, using some simplifying assumptions. The main hypotheses are: the aqueous phase is perfectly mixed, the drops of the organic phase are lumped into a plug-flow inner cylinder co-axial with the aqueous phase, and the organic phases under the sieve and on the top of the column are perfectly mixed also. The dynamic model of the extraction-back extraction column is, then, applied to the recovery of the hydrocarboxylic acids. The mathematical model, reduced through orthogonal collocation to a system of ordinary differential equations, was solved using a self-adaptive (RK)-type method. Its validation was done based on batch experimental data; the optimal model parameters (the specific mass transfer coefficients for both extraction and back-extraction zones), ensuring the agreement with the experiment, were found by means of a modified genetic algorithm technique. Then, a sensitivity analysis was done, to grasp the behaviour of the system with respect to the main operating parameters - the organic flow in the closed loop, the partition coefficient and the buffer volume.

Investigation of thermal performance of single basin solar still with soft drink cans filled with sand as a storage medium

2021 ◽  
pp. 1-31
Author(s):  
A.M. Khallaf ◽  
A.A. El-Sebaii ◽  
M.M. Hegazy
Keyword(s):  
Mathematical Model ◽  
Thermal Performance ◽  
Soft Drink ◽  
Model Parameters ◽  
Solar Still ◽  
Storage Material ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Basin Water ◽  
The Masses

Abstract Thermal performance of the single basin solar still (SBSS) with and without a storage material is presented experimentally and theoretically. New configuration of the SBSS by using soft drink cans filled with sand, fixed on the upper surface of the basin liner, as a sensible storage material is investigated. A mathematical model (using Pascal language) is developed to verify the thermal performance of the SBSS. Comparisons between experimental and theoretical (obtained from the mathematical model) results are carried out for validating the proposed mathematical model. Parameters affecting the thermal performance of the SBSS such as the masses of the basin water and storage material, heat transfer coefficients and top losses are investigated. The top losses (Ut) for the SBSS with sand is lower than that without sand by about 27.47%. The daily productivity (Pd) and efficiency (ηd) of the SBSS with sand is more than that without sand by about 31.44 and 23.12%, respectively. This experiment is environmentally friendly by using 126 of the used empty soft drink cans.

Modelling and experimental validation of enantioseparation of racemic phenylalanine via a hollow fibre-supported liquid membrane

2014 ◽  
Vol 68 (2) ◽  
Author(s):  
Tatchanok Prapasawat ◽  
Anchaleeporn Lothongkum ◽  
Ura Pancharoen
Keyword(s):  
Mathematical Model ◽  
Liquid Membrane ◽  
Equilibrium Constants ◽  
Enantiomeric Excess ◽  
Feed Solution ◽  
Hollow Fibre ◽  
Supported Liquid Membrane ◽  
Transfer Coefficients ◽  
Average Deviation ◽  
Feed Phase

AbstractThis paper reports on the enantioseparation of racemic phenylalanine or D-phenylalanine and Lphenylalanine via a hollow fibre-supported liquid membrane (HFSLM) and the results are compared with the mathematical model. The enantioseparation results, of 80 % and 73 %, showed the highest extraction and stripping of l-phenylalanine from the feed phase and the enantiomeric excess (% ee) of 60 % from 6 mmol L−1 of initial rac-phenylalanine in the feed solution. The optimum parameters were feed solution at pH 5, 6 mmol LL−1 of O,O′-dibenzoyl-(2S,3S)-tartaric acid ((+)-DBTA) as the extractant in octanol as the liquid membrane, and deionised water as the stripping solution. Equal flow-rates of feed and stripping solutions of 100 mL minL−1 were adjusted in a batch operation mode for 50 min at ambient temperature. From the calculation, the equilibrium constants of extraction (K ex) and mass transfer coefficients in the feed phase (k f) and in the liquid membrane phase (k m) were found to be 1.81 L mmol−2, 3.50 × 10−2 cm s−1, and 1.40 × 10−2 cm s−1, respectively. Finally, the change in concentrations of d,l-phenylalanine over time in the feed and stripping solutions by mathematical model were estimated and compared with the experimental results. The values thus calculated were in agreement with the experimental data with the average deviation of approximately 3 %.

scholarly journals A mathematical model for designing a reliable cellular hybrid manufacturing-remanufacturing system considering alternative and contingency process routings

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Amirreza Hooshyar Telegraphi ◽  
Akif Asil Bulgak
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Manufacturing Systems ◽  
Closed Loop ◽  
Sustainable Manufacturing ◽  
Critical Issue ◽  
Economic Benefits ◽  
Mixed Integer ◽  
Hybrid Manufacturing ◽  
Closed Loop Supply Chain

AbstractDue to the stringent awareness toward the preservation and resuscitation of natural resources and the potential economic benefits, designing sustainable manufacturing enterprises has become a critical issue in recent years. This presents different challenges in coordinating the activities inside the manufacturing systems with the entire closed-loop supply chain. In this paper, a mixed-integer mathematical model for designing a hybrid-manufacturing-remanufacturing system in a closed-loop supply chain is presented. Noteworthy, the operational planning of a cellular hybrid manufacturing-remanufacturing system is coordinated with the tactical planning of a closed-loop supply chain. To improve the flexibility and reliability in the cellular hybrid manufacturing-remanufacturing system, alternative process routings and contingency process routings are considered. The mathematical model in this paper, to the best of our knowledge, is the first integrated model in the design of hybrid cellular manufacturing systems which considers main and contingency process routings as well as reliability of the manufacturing system.

The Control of Vibration Transmissibility Using an Electrodynamic Actuator –Close-Loop Solution

2013 ◽  
Vol 436 ◽  
pp. 166-173
Author(s):  
A. Mihaela Mîţiu ◽  
Daniel Constantin Comeagă ◽  
Octavian G. Donţu
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Mechanical System ◽  
Closed Loop ◽  
Mechanical Systems ◽  
Vibration Transmissibility ◽  
Technical Solutions ◽  
The Mathematical Model

In this paper are presented some aspects of transmissibility control of mechanical systems with 1 DOF so that the effects of vibration on their action to be minimized. Some technical solutions that can be used for this purpose is analyzed. Starting from the mathematical model of an electro-mechanical system with 1 DOF, are identified the parameters which influence the effectiveness of the transmissibility control system using an electrodynamic actuator who work in "closed loop".

A multi-objective model for sustainable closed-loop supply chain of perishable products under two carbon emission regulations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Saman Esmaeilian ◽  
Dariush Mohamadi ◽  
Majid Esmaelian ◽  
Mostafa Ebrahimpour
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Life Cycle ◽  
Carbon Emission ◽  
Closed Loop ◽  
Perishable Products ◽  
Supply Chain Network ◽  
Closed Loop Supply Chain ◽  
Content Type ◽  
Trade Model

Purpose This paper aims to minimize the total carbon emissions and costs and also maximize the total social benefits. Design/methodology/approach The present study develops a mathematical model for a closed-loop supply chain network of perishable products so that considers the vital aspects of sustainability across the life cycle of the supply chain network. To evaluate carbon emissions, two different regulating policies are studied. Findings According to the obtained results, increasing the lifetime of the perishable products improves the incorporated objective function (IOF) in both the carbon cap-and-trade model and the model with a strict cap on carbon emission while the solving time increases in both models. Moreover, the computational efficiency of the carbon cap-and-trade model is higher than that of the model with a strict cap, but its value of the IOF is worse. Results indicate that efficient policies for carbon management will support planners to achieve sustainability in a cost-effectively manner. Originality/value This research proposes a mathematical model for the sustainable closed-loop supply chain of perishable products that applies the significant aspects of sustainability across the life cycle of the supply chain network. Regional economic value, regional development, unemployment rate and the number of job opportunities created in the regions are considered as the social dimension.

Closed Loop Identification by Optimization Method

2015 ◽  
Vol 1084 ◽  
pp. 636-641
Author(s):  
Valeriy F. Dyadik ◽  
Nikolay S. Krinitsyn ◽  
Vyacheslav A. Rudnev
Keyword(s):  
Closed Loop ◽  
Uranium Hexafluoride ◽  
Optimization Method ◽  
Model Parameters ◽  
Control Loop ◽  
Loop Control ◽  
Identification Method ◽  
Closed Loop Control System ◽  
Closed Loop Identification ◽  
Loop Control System

The article is devoted to the adaptation of the controller parameters during its operation as a part of a control loop. The possibility to identify the parameters of the controlled plant model in the closed control loop has been proved by a computer simulation. The described active identification method is based on the response processing of the closed loop control system to standard actions. The developed algorithm has been applied to determine the model parameters of the flaming fluorination reactor used for the production of uranium hexafluoride. Designed identification method improves the quality of the product and the efficiency of the entire production.

scholarly journals The identification of a device based on a Peltier element by the least squares method

2020 ◽  
pp. 17-27
Author(s):  
Vladimir Grinkevich ◽  
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Control Object ◽  
Object Identification ◽  
Model Parameters ◽  
Peltier Element ◽  
Transport Delay ◽  
Non Linear ◽  
The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

scholarly journals The Concentration of Digoxin Activity after Intravenous in Three Compartments Mathematical Model

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3653-3657
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Digoxin Concentration ◽  
Compartment Model ◽  
System Of Equations ◽  
Transfer Coefficients ◽  
Linear Ordinary Differential Equations ◽  
Concentration Time ◽  
The Laplace Transform ◽  
Three Compartment Model

Present paper is designed to compare the distribution of digoxin in three compartment model administered through an intravenous (i.v). These models under consideration is denoted by a system of non-linear ordinary differential equations. The Eigenvalue and the Laplace transform methods were used to solve the system of equations. Digoxin was administered to five subjects through Intravenous then, the serum digoxin concentrations were measured respectively over a period of 72 hours. The transfer coefficients were obtained from observed digoxin concentrations using method of residuals and the variation of digoxin concentration – time curves plotted using MATLAB.

scholarly journals Interphase Surface Stability in Liquid-Liquid Membrane Contactors Based on Track-Etched Membranes

Membranes ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 949
Author(s):  
Stepan Bazhenov ◽  
Olga Kristavchuk ◽  
Margarita Kostyanaya ◽  
Anton Belogorlov ◽  
Ruslan Ashimov ◽  
...  
Keyword(s):  
Pressure Drop ◽  
Porous Structure ◽  
Pore Size ◽  
Aqueous Phase ◽  
Liquid Membrane ◽  
Target Component ◽  
Interphase Surface ◽  
Asymmetric Membrane ◽  
Interface Stability ◽  
Membrane Contactors

A promising solution for the implementation of extraction processes is liquid–liquid membrane contactors. The transfer of the target component from one immiscible liquid to another is carried out inside membrane pores. For the first time, highly asymmetric track-etched membranes made of polyethylene terephthalate (PET) of the same thickness but with different pore diameters (12.5–19 nm on one side and hundreds of nanometers on the other side) were studied in the liquid–liquid membrane contactor. For analysis of the liquid–liquid interface stability, two systems widely diverging in the interfacial tension value were used: water–pentanol and water–hexadecane. The interface stability was investigated depending on the following process parameters: the porous structure, the location of the asymmetric membrane in the contactor, the velocities of liquids, and the pressure drop between them. It was shown that the stability of the interface increases with decreasing pore size. Furthermore, it is preferable to supply the aqueous phase from the side of the asymmetric membrane with the larger pore size. The asymmetry of the porous structure of the membrane makes it possible to increase the range of pressure drop values between the phases by at least two times (from 5 to 10 kPa), which does not lead to mutual dispersion of the liquids. The liquid–liquid contactor based on the asymmetric track-etched membranes allows for the extraction of impurities from the organic phase into the aqueous phase by using a 1% solution of acetone in hexadecane as an example.

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