• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.673-682
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• 2020

For the recently defined notion of strongly lifting modules, it has been shown that a direct sum is not, in general, strongly lifting. In this paper we investigate the question: When are the direct sums of strongly lifting modules, also strongly lifting? We introduce the notion of a relatively strongly projective module and use it to show if M = M1 ⊕ M2 is amply supplemented, then M is strongly lifting if and only if M1 and M2 are relatively strongly projective and strongly lifting. Also, we consider when an arbitrary direct sum of hollow (resp. local) modules is strongly lifting.

• Membrane and Water Treatment
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• v.8 no.2
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• pp.137-147
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• 2017

A water treatment utility in South Korea operates a large system of pressurized hollow fiber membrane (PHFM) modules. The optimal selection of membrane module for the full scale plant was critical issue and carried out using Risk-based Life Cycle Cost (RbLCC) analysis based on the historical data of operation and maintenance. The RbLCC analysis was used in the process of decision-making for replacing aged modules. The initial purchasing cost and the value at risk during operation were considered together. The failure of modules occurs stochastically depending on the physical deterioration with usage over time. The life span of module was used as a factor for the failure of Poisson's probability model, which was used to obtain the probability of failure during the operation. The RbLCC was calculated by combining the initial cost and the value at risk without its warranty term. Additionally, the properties of membrane were considered to select the optimum product. Results showed that the module's life span in the system was ten years (120 month) with safety factor. The optimum product was selected from six candidates membrane for a full scale water treatment facility. This method could be used to make the optimum and rational decision for the operation of membrane water purification facility.

• Environmental Engineering Research
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• v.24 no.2
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• pp.347-353
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• 2019

Although membrane distillation (MD) has great promise for desalination of saline water sources, it is crucial to improve its thermal efficiency to reduce the operating cost. Accordingly, this study intended to examine the thermal energy efficiency of MD modules in a pilot scale system. Two different modules of hollow fiber membranes were compared in direct contact MD mode. One of them was made of polypropylene with the effective membrane area of $2.6m^2$ and the other was made of polyvinylidene fluoride with the effective membrane area of $7.6m^2$. The influence of operation parameters, including the temperatures of feed and distillate, feed flow rate, and distillate flow rate on the flux, recovery, and performance ratio (PR), was investigated. Results showed that the two MD membranes showed different flux and PR values even under similar conditions. Moreover, both flow rate and temperature difference between feed and distillate significantly affect the PR values. These results suggest that the operating conditions for MD should be determined by considering the module properties.

• Korean Chemical Engineering Research
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• v.60 no.1
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• pp.51-61
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• 2022

Gas separation via hollow fibre membrane modules (HFMM) is deemed to be a promising technology for natural gas sweetening, particularly for lowering the level of carbon dioxide (CO₂) in natural gas, which can cause various problems during transportation and process operation. Separation performance via HFMM is affected by membrane properties, module specifications and operating conditions. In this study, a mathematical model for HFMM is developed, which can be used to assess the effects of the aforementioned variables on separation performance. Appropriate boundary conditions are imposed to resolve steady-state values of permeate variables and incorporated in the model equations via an iterative numerical procedure. The developed model is proven to be reliable via model validation against experimental data in the literature. Also, the model is capable of capturing axial variations of process variables as well as predicting key performance indicators. It can be extended to simulate a large-scale plant and identify an optimal process design and operating conditions for improved separation efficiency and reduced cost.

• Membrane and Water Treatment
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• v.3 no.3
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• pp.141-149
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• 2012

The aeration provided in a Submerged Membrane Bioreactor (SMBR) improves membrane filtration by creating turbulence on the membrane surface and reducing membrane resistance. However, conventional hollow fiber membrane modules are generally packed in a vertical orientation which limits membrane scouring efficiency, especially when aeration is provided in the axial direction. In the present research, 3 innovative hollow-fiber membrane modules, each with a different membrane orientation, were developed to improve membrane scouring efficiency and enhance permeate flux. Pilot testing was performed to investigate the permeate flux versus time relationship over a 7-day period under different intermittent modes. The results indicated that the best module experienced an overall permeate flux decline of 3.3% after 7 days; the other two modules declined by 13.3% and 18.3%. The lower percentage of permeate flux decline indicated that permeate productivity could be sustained for a longer period of time. As a result, the operational costs associated with membrane cleaning and membrane replacement could be reduced over the lifespan of the module.

• Membrane Journal
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• v.26 no.2
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• pp.159-165
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• 2016

Polyimide hollow fiber membrane modules were prepared in order to investigate the process of multi stage gas separation. The modules performance was carried out using 50/50 of $N_2/SF_6$ mixed gas. The membrane modules has been tested for measuring gas flow rate and concentration under various stage cut at 0.5 MPa. The membrane modules showed a high recovery ratio at the same stage cut as $N_2/SF_6$ selectivity increased. Two stage process was fulfilled for improving $SF_6$ recovery ratio and $SF_6$ concentration. Eventually, two stage process showed higher performance of $SF_6$ recovery ratio and concentration ($SF_6$ recovery ratio = 95%, $SF_6$ conc. = 98%).

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• Proceedings of the Membrane Society of Korea Conference
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• 1997.04a
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• pp.87-109
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• 1997

Reverse osmosis(R/O), ultrafiltration(UF) and microfiltration (MF) processes are widely used for water treatment. In the seminar, characteristics of typical membrane modules including tubular, hollow fiber, plate and frame and spiral wound types will be discussed in detail. The design methods based on hydrodynamics for hollow fiber and spiral wound modules will be introduced analytically. Concentration polarization (CP) and membrane fouling mechnism as well as the techniques for CP reduction will be handled. The CP control techniques contain chemically modified membrane surface, pretreatment of feed water, operation of low trans-membrane pressure, chemical or physical cleaning methods and artificial production of various fluid turbulences near the membrane surface, etc. In especially, the recent commercial membrane modules for CP control including module rotation, vibration and Taylor or Dean vortex system will be introduced and discussed in detail.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.445-453
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• 2005

We say that a module M is weak lifting if M is supplemented and every supplement submodule of M is a direct summand. The module M is called lifting, if it is weak lifting and amply supplemented. This paper investigates the structure of weak lifting modules and lifting modules having small radical over commutative noetherian rings.

• Journal of Climate Change Research
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• v.7 no.3
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• pp.249-256
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• 2016

Porous $Al_2O_3$ hollow fiber membranes were successfully prepared by dry-wet spinning/sintering method. The SEM image shows that the $Al_2O_3$ hollow fiber membrane consists mostly of sponge pore structure. The contact angle and the breakthrough pressure were $126^{\circ}$ and 1.91 bar, respectively. This results indicate that the $Al_2O_3$ hollow fiber membranes were successfully modified to hydrophobic surface. The hydrophobic modified $Al_2O_3$ hollow fiber membranes were assembled into a membrane contactor system to separate $CO_2$ from a model gas mixture of the flue gas at elevated gas velocity. The $CO_2$ absorption flux was enhanced when the gas velocity increased from $1{\times}10^{-3}$ to $6{\times}10^{-3}$ m/s. Whereas the $CO_2$ absorption flux was decreased with the number of hollow fiber membrane of a module because of the concentration polarization. Furthermore, we developed an lab-scale $Al_2O_3$ hollow fiber membrane contactor modules and their system (i.e., $CO_2$ absorption using the $Al_2O_3$ membrane and monoethanolamine (MEA)) that could dispose of over $0.02Nm^3/h$ mixture gas (15% $CO_2$) with the removal efficiency higher than 95%. The results can be useful in a field of the membrane contactor for $CO_2$ separation, helping to design and extend a equipment.