\r\n\t \r\n\tThe concepts of sets emerges naturally in the human mind, being an abstract concept created by our human reasoning. An example is the set of natural numbers, which can be seen as an immediate consequence of the notion of sets. \r\n\t \r\n\tHowever, when the human mind creates abstract concepts, such as numbers, which are often associated with concrete concepts; However, in some cases, it is impossible to count the number of elements of a set, even knowing that it has a finite amount of elements. The number of residences in the world or stars in the sky is a finite number, no matter how amazingly large. Thus, one of the fundamental questions of the sets theory arises that is "Does the order we use to count things not affect the result?". \r\n\t \r\n\tThere are many questionings of this kind that arise. Despite the protests of several lines of research, such as constructivists and intuitionists, the pillars of the theory of sets developed by Cantor, Zermelo, Frankel, and Von Neumann, served as the basis for the rationale of mathematics. The fundamental idea is to use sets to define all mathematical objects as sets. Everything is set! \r\n\t \r\n\tThis book aims to show new advances and representations in sets theory, asking questions still open and explaining complex axioms. Applications from sets theory to real-world representation problems can also be presented. Philosophical problems and new modeling can also be addressed.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"73611199b1ada8e6e847165c1002dcbb",bookSignature:"Prof. Germano Lambert-Torres",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9328.jpg",keywords:"Algebra of classes, Family of Classes,Natural numbers, Equipotence of sets, Operations, Ordering, Theory of Ordinals and Cardinals, Normal form, Epsilon numbers, Independence results, Göedel Theorems, Fuzzy sets, Rough sets, Paraconsistent logic",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 18th 2019",dateEndSecondStepPublish:"March 10th 2020",dateEndThirdStepPublish:"May 9th 2020",dateEndFourthStepPublish:"July 28th 2020",dateEndFifthStepPublish:"September 26th 2020",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"112971",title:"Prof.",name:"Germano",middleName:null,surname:"Lambert-Torres",slug:"germano-lambert-torres",fullName:"Germano Lambert-Torres",profilePictureURL:"https://mts.intechopen.com/storage/users/112971/images/system/112971.jpg",biography:"Germano Lambert-Torres is a Professor at the Instituto Gnarus. He received his Ph.D. degree in Electrical Engineering from the Ecole Polytechnique de Montreal, Canada, in 1990. From 1983 to 2012, he was with the Electrical Engineering Department, Itajuba Federal University (UNIFEI), where he was also the Dean of the Research and Graduate Studies, from 2000 to 2004. Since 2010, he has been the Director of R&D, PS Solucoes, Itajuba. He also serves as a consultant for many utility companies in Brazil and South America, and has taught numerous IEEE tutorials in the USA, Europe, and Asia. He is the author/editor or coauthor of nine books, more than 30 book chapters, and 50 transactions articles on intelligent systems and nonclassical logic.",institutionString:"Gnarus Institute",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"6",totalChapterViews:"0",totalEditedBooks:"0",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"15",title:"Mathematics",slug:"mathematics"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"247041",firstName:"Dolores",lastName:"Kuzelj",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/247041/images/7108_n.jpg",email:"dolores@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. Whether that be identifying an exceptional author and proposing an editorship collaboration, or contacting researchers who would like the opportunity to work with IntechOpen, I establish and help manage author and editor acquisition and contact."}},relatedBooks:[{type:"book",id:"1591",title:"Infrared Spectroscopy",subtitle:"Materials Science, Engineering and Technology",isOpenForSubmission:!1,hash:"99b4b7b71a8caeb693ed762b40b017f4",slug:"infrared-spectroscopy-materials-science-engineering-and-technology",bookSignature:"Theophile Theophanides",coverURL:"https://cdn.intechopen.com/books/images_new/1591.jpg",editedByType:"Edited by",editors:[{id:"37194",title:"Dr.",name:"Theophanides",surname:"Theophile",slug:"theophanides-theophile",fullName:"Theophanides Theophile"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3092",title:"Anopheles mosquitoes",subtitle:"New insights into malaria vectors",isOpenForSubmission:!1,hash:"c9e622485316d5e296288bf24d2b0d64",slug:"anopheles-mosquitoes-new-insights-into-malaria-vectors",bookSignature:"Sylvie Manguin",coverURL:"https://cdn.intechopen.com/books/images_new/3092.jpg",editedByType:"Edited by",editors:[{id:"50017",title:"Prof.",name:"Sylvie",surname:"Manguin",slug:"sylvie-manguin",fullName:"Sylvie Manguin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3161",title:"Frontiers in Guided Wave Optics and Optoelectronics",subtitle:null,isOpenForSubmission:!1,hash:"deb44e9c99f82bbce1083abea743146c",slug:"frontiers-in-guided-wave-optics-and-optoelectronics",bookSignature:"Bishnu Pal",coverURL:"https://cdn.intechopen.com/books/images_new/3161.jpg",editedByType:"Edited by",editors:[{id:"4782",title:"Prof.",name:"Bishnu",surname:"Pal",slug:"bishnu-pal",fullName:"Bishnu Pal"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"72",title:"Ionic Liquids",subtitle:"Theory, Properties, New Approaches",isOpenForSubmission:!1,hash:"d94ffa3cfa10505e3b1d676d46fcd3f5",slug:"ionic-liquids-theory-properties-new-approaches",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/72.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1373",title:"Ionic Liquids",subtitle:"Applications and Perspectives",isOpenForSubmission:!1,hash:"5e9ae5ae9167cde4b344e499a792c41c",slug:"ionic-liquids-applications-and-perspectives",bookSignature:"Alexander Kokorin",coverURL:"https://cdn.intechopen.com/books/images_new/1373.jpg",editedByType:"Edited by",editors:[{id:"19816",title:"Prof.",name:"Alexander",surname:"Kokorin",slug:"alexander-kokorin",fullName:"Alexander Kokorin"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"57",title:"Physics and Applications of Graphene",subtitle:"Experiments",isOpenForSubmission:!1,hash:"0e6622a71cf4f02f45bfdd5691e1189a",slug:"physics-and-applications-of-graphene-experiments",bookSignature:"Sergey Mikhailov",coverURL:"https://cdn.intechopen.com/books/images_new/57.jpg",editedByType:"Edited by",editors:[{id:"16042",title:"Dr.",name:"Sergey",surname:"Mikhailov",slug:"sergey-mikhailov",fullName:"Sergey Mikhailov"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"371",title:"Abiotic Stress in Plants",subtitle:"Mechanisms and Adaptations",isOpenForSubmission:!1,hash:"588466f487e307619849d72389178a74",slug:"abiotic-stress-in-plants-mechanisms-and-adaptations",bookSignature:"Arun Shanker and B. 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1. Introduction
1.1. Hybrid desalination concept
Hybrid technology is defined as any combination of thermal and membrane processes in seawater desalination systems. So far, the two technologies have evolved rather independently with some degree of competition. Traditionally, in co-generation market applications, thermal desalination has succeeded in establishing a stronghold where large capacities are needed, energy costs are low, and seawater quality is challenging. However, in recent years, membrane systems have also succeeded in grabbing a larger share of the world seawater desalination market, mainly as a result of the progress made in membrane and energy recovery technologies. Realizing the potential benefits and challenges faced by both technologies on their own, designers have been looking for ways to synergize and combine the two technologies in optimum configurations, which promise to further reduce the total cost of seawater desalination.
Several studies have been published over the past 20 [1-14] years addressing the potential of integrating hybrid desalination systems. Coupling schemes worth noting for hybrid systems include RO preheating using condenser heat reject of the associated distillation unit; adding thermal vapour compression to MED systems; the use of membrane filtration (NF) upstream of MSF, MED, and RO systems; brine recirculation coupling; product blending; and the use of common intake and outfall systems.
To date, commercially available hybrid plants are of the simple non-integrated type. They may share common systems such as intake and outfall facilities, but otherwise they run independently at the same site. Product water of both membrane and thermal plants are usually blended to meet the international standards water quality specifications. Examples of existing hybrid plants include Jeddah, Al-Jubail, and Yanbu in Saudi Arabia. Recently, a power and water plant has been designed and built by Doosan in Fujairah (UAE). This plant produces 500 MW of net electricity to the grid and 100,000 MIGD of fresh water, 63% of which is produced by MSF with the balance produced by RO [1].
1.2. NF’s role in desalination
NF, in particular, has been advocated as a pretreatment option upstream of a thermal desalination unit [2-8]. Due to small pore size and charge at the surface of the membrane, NF is known to remove divalent ions, including a fraction of scale-producing hardness and salts, allowing in principle at least a possible increase in top brine temperature and promising improved steam economy. Studies on NF-MSF pilot tests claim scale-free operation for 1,200 hours with top brine temperatures reaching 130°C, reporting an improvement in recovery from 30% for stand-alone MSF to 70% with NF [2-8]. The integration of NF –MED system is under pilot investigation by Saline Water Desalination Research Institute (SWDRI) with Sasakura (a Japanese-based consortium) [15]. Implementation of dual-stage NF has been successful evaluated at Long Beach, California [16]. From the present analysis, NF will play a crucial role in desalination, provided that the cost of NF membrane would be decreased. Efficient removal of boron has also been reported [16]. However, the reliability and economic viability of such a design need to be confirmed, considering the higher thermal and pressure load implied by the design and the additional capital, energy, and operation and maintenance costs of membrane pre-treatment components. Adding to the uncertainty are increased risks for corrosion and the long-term reliability of such a system.
1.3. FO role in desalination
The role of using forward osmosis (FO) as a pre-treated method to the existing thermal desalination MSF/MED plants is to reduce divalent ions that cause hard-scale deposition at elevated temperature. The removal of the divalent ions, such as CaSO4, from the MSF feed enables to increase the desalination process temperature greater than 110°C. Consequently the plant performance and productivity will increase. Due to the removal of the ions which cause scale deposit, the chemical additive consumption will be decreases. In the MSF process due to working at higher temperature, hard scale, such as calcium sulphate, is formed. As calcium sulphate is two orders of magnitude more soluble than calcium carbonate, the sulphate is much less likely to drop out of solution when both are present.
In the light of the recent development in the membrane filtration technologies, the cost of seawater pretreatment can be reduced if FO membranes were used with/without NF. The novel application of FO membrane for seawater filtration requires, firstly, retrofitting the FO system to the thermal desalination unit. Secondly, it also requires finding a suitable draw solution that would reduce the cost of FO pre-treatment. Fortunately, the current FO membranes exhibit high water permeability and rejection rate, which make them an ideal solution for seawater pretreatment [17]. A novel hybrid FO-thermal desalination system to remove scale deposit elements from seawater to the thermal units, is presented [17-18]. The performance of the thermal evaporator was evaluated after introducing the FO pretreatment. The scale deposition on the thermal unit was estimated by using special software to predict the precipitation on inversely soluble metal ions on the heat exchangers [17-18].
1.4. Objective
This chapter addresses the role of using FO or NF as a pre-treated method to the existing thermal desalination plants. The target of this hybridization is to reduce divalent ions that cause hard-scale deposition at elevated temperature. The separation of divalent ion enables the increase of the desalination process temperature greater than 110°C, which consequently increases plant performance and productivity, as well as reduces the chemical consumption.
2. Process description
2.1. MSF-RO hybrid
The simple type refers to co-located thermal and membrane systems that may share some common systems on site. This in turn facilitate blended to product water specifications, but otherwise are running independently. Examples include the Fujairah plant and three Saudi plants in Jeddah, Al-Jubail, and Yanbu. The Fujairah plant [1], representing a simple hybrid type, was constructed by Doosan Heavy Industries and is currently considered the largest existing hybrid type. The plant is rated at 100 MIGD, of which 63% are produced by MSF and 37% by RO. Featuring a combined cycle system, it also generates 500 MW to the grid. The thermal part of the plant includes five MSF evaporators rated at 12.5 MIGD each, with a top brine temperature of 110◦C. The membrane part includes two RO passes, using a conventional pretreatment system and energy recovery devices of the Pelton type. A specification of 200 PPM as the maximum water product salinity was met by the design.
Another option of a hybrid type is to improve the membrane performance. This type includes the integration of hybrid membrane and thermal systems, with the aim of improving membrane recovery by preheating the RO feed using heat reject from the thermal unit as shown in Figure (1). Higher temperatures are known to improve membrane flux, mainly as a result of reduced viscosity. Several investigators examined the effects of preheating in pilot tests, and about 3% of recovery improvement is reported per degree Celsius [19]. This should, however, be weighed against potential negative effects of high temperatures on membrane performance, in particular compaction damage. Membrane manufacturers have traditionally set an upper temperature limit of 40◦C for the use of their membranes, and it is not clear how close to this limit operation should be, in order to optimize life-cycle membrane performance and costs. The measure is particularly useful in winter when seawater temperatures are reduced.
Figure 1.
Process flow diagram of hybrid RO-MSF process
Preheating the Fujairah RO feed in winter is an example of integrated hybrid operation, representing type 2. A 10°C increase from 23°C to 33°C for an RO unit equivalent in capacity to the Fujairah plant would increase recovery by about 30% and, therefore, reduce feed pressure requirements. This preheating feature could then be made to good use in the winter when seawater temperatures in the Gulf drop by 15–20°C.
2.2. NF-MSF process
This type includes the integration of hybrid membrane and thermal systems with the objective of improving the gain output ratio (GOR) and steam economy of the thermal system (see Figure 2). The GOR is a function of the available temperature range and can, therefore, be improved by increasing the top brine temperature (TBT). Traditionally, the top brine temperature is limited to 110 °C for MSF and is limited to 65◦C for MED. This practice, in addition to chemical dosing and mechanical cleaning, is necessary to minimize scale deposition on heat transfer surfaces. Some investigators have advocated the use of NF membrane upstream of the thermal system as a pretreatment step to reduce scaling hardness and additionally some salt. This would, in principle, allow operation at higher temperatures, without increased scaling. SWCC investigators have tested a hybrid NF/MSF pilot unit running at a top brine temperature of 130°C for a period of 1,200 hours and reported a doubling in the recovery with no observed scale formation [10].
Figure 2.
Process flow diagram of hybrid NF-MSF process
2.3. FO-MSF
Figure 3 shows hybrid FO-multi stage flash (FO-MSF) system for high TBT MSF. In this type of hybrid system, the brine reject from the thermal desalination process will be considered as a draw solution, while the cooling seawater exiting from the MSF heat rejection section will be used as a feed solution. Permeate water will transport across the FO membrane from the feed to the draw solution side while monovalent and multivalent ions are rejected by the FO membrane. After leaving the FO membrane, the concentrated seawater is dumped back to the sea. Simultaneously, the diluted draw solution from the FO process is circulated to the MSF recovery section. Inside the MSF plant, fresh water is extracted from the draw solution by evaporation and is condensed in the consecutive MSF chambers. The distilled water is collected at the last stage and directed to the distilled tank. The un-flashed brine through MSF stages (brine pool) is collected in the last stage of MSF evaporator at high salinity and then is directed to the FO as a draw solution.
Figure 3.
Process flow diagram of hybrid FO-MSF process
2.4. FO-MED
Figure 4 shows the hybrid FO-multi effect distillation (FO-MED) system for high TBT MED. In this type of hybrid system, the brine reject from the last effect will be considered as a draw solution stream, while the condenser cooling seawater will be used as a feed solution stream. Permeate water will transport across the FO membrane from the feed to the draw solution side while monovalent and multivalent ions are rejected by the FO membrane. After leaving the FO membrane, the concentrated seawater is dumped back to the sea water. Simultaneously, the diluted draw solution from the FO process is circulated to the MED evaporator as a makeup feed. Inside the MED evaporator, fresh water is extracted from the draw solution by evaporation and is condensed in the consecutive MED effect. The distilled water is collected at the last effect and is directed to the distilled tank. The brine (un-evaporated) through MED effect is collected in the last effect at a high salinity is directed to the FO again as a draw solution.
Figure 4.
Process flow diagram of hybrid FO-MED process
3. Methodology
3.1. Mathematical model development of NF
Figure 5 illustrates the input and output parameters used for the mass and energy balance equations of the NF membrane [13-14].
Figure 5.
Schematic diagram of the NF membrane streams
Mass balance is written as follows:
Wf,j=Wp,j+Wb,jE1
\n\t\t\t\t
Sf,j=Sp,j+Sb,jE2
\n\t\t\t\t
The following relation defines the rate of water passage through a semipermeable membrane [14]:
Wp,j=(ΔPj−σΔπj)×Kw×Aj×TCF×FF×ρp,jE3
\n\t\t\t\t
ΔPj=Pj__−Pp,jE4
\n\t\t\t\t
Δπj=πj_−πp,jE5
\n\t\t\t\t
Pj_=0.5(Pf,j+Pb,j)E6
\n\t\t\t\t
As the seawater salt concentrations ratio is almost constant, an approximation for value in kPa can be given as [13]:
π=6.895×38.5×CfbNaCl×(T+273)1000+CfbNaClE7
\n\t\t\t\t
CfbNaCl=0.934348×Cfb−0.54169E8
\n\t\t\t\t
The rate of salt flow through the membrane is defined as:
Where, the temperature factor correction (TCF) is calculated using the following equations [14]:
TCF=e8.859×T−25T+273, forT≥25°CE11
\n\t\t\t\t
TCF=e11.678×T−25T+273, forT≥25°CE12
\n\t\t\t\t
Cp,j=Sp,j×ρp,j/(Sp,j+Wp,j)E13
\n\t\t\t\t
A material balance within the mass transfer boundary layer near the membrane wall between the solute carried to the membrane by convection and the solute carried away by diffusion yields an expression that quantifies concentration polarization:
φ=Cm−CpCb−Cp=eJw/kE14
\n\t\t\t\t
The Umm-Lujj NF-RO plant [20] is considered as a case study to verify the mathematical model of the NF membrane equation (1-14), as well as to estimate the permeate constant Kw and the solute constant Ks.
This plant consists of 27 pressure vessels and six NF elements per vessel. The feed characteristic is 360 m3/hr, the temperature is 32°C, and the salinity is 45.46 g/l. The applied feed pressure is 25 bars. The data from the Umm-Lujj plant, shown in Table (1), are used as the input data of VDS [21-25] software as shown in Figure 6.
Figure 6.
VDS interface of the NF system with pressure exchanger
The VDS simulates the Umm-Lujj plant of NF to estimate the permeate production and the exact value of the membrane constants Kw and Ks. After several runs, the membrane water permeability Kw of the considered NF membrane is determined as follows:
Kw=5.8×10−9m3/m2.s.kPaE15
\n\t\t\t\t
The membrane salt permeability coefficient Ks is estimated as follows:
Ks=9×10−8E16
\n\t\t\t\t
Using the estimated values Kw and Ks, the VDS results are compared against the typical plant as shown in Table (1). The comparison results show a good agreement between the VDS results and the typical real plant.
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\tVariable\n\t\t\t
\n\t\t\t
\n\t\t\t\tVSP results\n\t\t\t
\n\t\t\t
\n\t\t\t\tUmm-Lujj\n\t\t\t
\n\t\t\t
\n\t\t\t\t% Error\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
Feed flow rate, m3/hr, *
\n\t\t\t
360
\n\t\t\t
360
\n\t\t\t
-
\n\t\t
\n\t\t
\n\t\t\t
Feed salinity, TDS, g/l, *
\n\t\t\t
45.46
\n\t\t\t
45.46
\n\t\t\t
-
\n\t\t
\n\t\t
\n\t\t\t
Stages No.*
\n\t\t\t
1
\n\t\t\t
1
\n\t\t\t
-
\n\t\t
\n\t\t
\n\t\t\t
No. of pressure vessels, *
\n\t\t\t
27
\n\t\t\t
27
\n\t\t\t
-
\n\t\t
\n\t\t
\n\t\t\t
Feed temperature, °C, *
\n\t\t\t
32
\n\t\t\t
32
\n\t\t\t
-
\n\t\t
\n\t\t
\n\t\t\t
Fouling factor, *
\n\t\t\t
0.95
\n\t\t\t
NA
\n\t\t\t
-
\n\t\t
\n\t\t
\n\t\t\t
Feed pressure, bar, *
\n\t\t\t
25
\n\t\t\t
25
\n\t\t\t
-
\n\t\t
\n\t\t
\n\t\t\t
Elements No. per vessel, *
\n\t\t\t
6
\n\t\t\t
6
\n\t\t\t
-
\n\t\t
\n\t\t
\n\t\t\t
Permeate flow rate, m3/hr
\n\t\t\t
245
\n\t\t\t
234
\n\t\t\t
4.7%
\n\t\t
\n\t\t
\n\t\t\t
Recovery ratio
\n\t\t\t
0.68
\n\t\t\t
0.65
\n\t\t\t
4.6%
\n\t\t
\n\t\t
\n\t\t\t
Permeate salinity, TDS, mg/l
\n\t\t\t
29.11
\n\t\t\t
28.26
\n\t\t\t
3%
\n\t\t
\n\t
Table 1.
Comparison between VDS and Umm-Lujj typical results
*Input data to the VDS
The VDS program is used to size the NF system to produce 226 m3/hr, which represents one-third of the makeup feed, which is required for 1 MIGD MSF. The required number of pressure vessels is calculated as 29 with 174 membrane elements. The calculated system recovery ratio is 65%. The high-pressure pump is assigned by 25 bars. Three units of pressure exchangers are used to recover an electrical energy of 0.07 MW. Each unit’s capacity is 44 m3/hr, and the percentage of salt increase is only 4.6%. The net pumping power required is 0.21 MW, and the specific power consumption is 0.94 kWh/m3.
3.2. Mathematical model of forward osmosis (FO)
Forward osmosis is the transport of water across a selectively permeable membrane from a region of higher water chemical potential (feed solution) to a region of lower water chemical potential (draw solution). Consequently, a less concentrated draw solution is being produced, which may be further treated to extract freshwater. Obviously, there are two key problems that must be solved to make the technology go out of the laboratory. One is continued improvement and optimization of the selectively permeable membrane, which allows passage of water but rejects most solute molecules or ions. The other is the identification of optimal osmotic agents and its corresponding recovery processes for the supply of the osmosis pressure difference, which is the driving force of the FO process. However, the FO membrane water flux is far lower than the anticipated when the membrane used is asymmetric. The primary reason for this finding is the fact that both FO are accompanied by internal concentration polarization (ICP) as shown in Figure 7.
Figure 7.
Concentration profile in asymmetrical FO membrane
In the work of Jung et al. [26], FO performance (permeate flux and recovery rate) of a 10 cm ×10 cm plate and frame type membrane is investigated via a numerical simulation based on the mass conservation theorem. The FO membrane orientation, flow direction of feed and draw solutions, flow rate, and solute resistivity (K) are simulated. The case of draw solution facing the active layer displays a relatively higher performance than the feed solution facing the active layer [26]. The numerical results showed that the membrane performance is much more sensitive to the physical membrane property parameter rather than the flow rate and flow direction. However, the simulation methodology does not consider fouling and reverse solute diffusion. Also, the performance of the FO in a relatively large size needs to be explored to come up with a concrete recommendation to the commercialization phase.
A simple schematic of the FO process is shown in Figure 8. The mathematical model of FO membrane is developed as shown in equations (17-26). By knowing the specifications of the FO membrane,, and the membrane area, the outlet stream can be calculated.
Figure 8.
Schematic of the FO membrane process
WDS,outlet−WDS,inlet=WpE17
\n\t\t\t\t
SDS,out−SDS,inlet=SpE18
\n\t\t\t\t
WFS,in−WFS,out=WpE19
\n\t\t\t\t
SFS,in−SFS,out=SpE20
\n\t\t\t\t
Wp=Jw×A×ρE21
\n\t\t\t\t
Sp=Js×AE22
\n\t\t\t\t
The general flux equation in the FO process is
Jw=A(πD−πF)E23
\n\t\t\t\t
where A is the water permeability coefficient, and and denote the osmotic pressures of the draw and feed solution, respectively. The osmotic pressure can be determined by the modified Van’t Hoff equation as:
Δπ=NionRgTΔCMwE24
\n\t\t\t\t
where T, and indicate the ionization number of the solution, the ideal gas constant, the absolute temperature, the salt concentration difference of the solution across the membrane, and the molecular weight of the salt, respectively. For asymmetrical membrane, internal ICP occurs within the porous support as shown in Figure 7. However, when the reverse solute is considered [27], and for the case of the draw solution facing the porous layer, the water flux and solute flux are:
The water flux and reverse solute equations are difficult to solve analytically because these equations are dependent on water flux and solute passage including in concentration polarization terms. Thus, using a program to solve these equations will be presented.
The FO is still facing many challenges such as internal concentration polarization, which requires breakthrough in the molecular design of high-performance FO membrane. On the other hand, development of draw solution with low cost and low energy consumption required for recovery is urgently needed. To mitigate ICP, the FO membranes must have characteristics of high permeability and hydrophobicity with a small structure parameter, while the preferred draw solutes must have diffusion coefficient, reasonable molecular size, and low viscosity [52].
The VDS Software interface is developed to consider a case study as shown in Figure 9. As shown in Figure 9, the specified feed solution of (1680 t/h and 45 g/l) is pumped to the FO membrane against a draw solution (NaCl) (1200 t/h and 90 g/l). Three elements per vessel are arranged. Two pressure vessels are placed in parallel. The VDS simulated the case, and the results are presented in the same interface as shown in Figure 9. The diluted flow rate is calculated as 1744 t/h and 64.34 g/l, while the concentrated feed solution is calculated as 1135.8 t/h and 66.46 g/l. Based on these calculations, the system recovery ratio is calculated as 45%, and the specific power consumption is calculated as 0.55 kWh/m3. So far, the effect of concentration polarization is not considered yet.
Figure 9.
Interface of VDS software for FO process
4. Technoeconomic analysis
4.1. NF-MSF
The first MSF of 0.5 MGD per unit evaporator was built in 1957 in Kuwait using the once through MSF-OT configuration by the Westinghouse Company [28]. The design was modified according to the recommendation of the client, the Ministry of Electricity and Water, in Kuwait and of engineers for reliable operation. For some time, the market was dominated by the once through (MSF-OT) due its simplicity and high thermodynamic efficiency. However, due to high oxygen and CO2 gas liberation in addition to large amount of feed water to be pre-treated, the market was forced to shift to the brine recirculation configuration (MSF-BR). The first 19-stage 1 MGD MSF-BR plant was built by Weir Company in 1959 in Kuwait [28]. The developed specifications led to more reliable, easy-to-operate-and-maintain, and longer life units. Now, the MSF evaporator production capacity was increased dramatically through the years to reach 20 MGD in UAE, and designs of 25-30 MIGD are available. The disadvantage of the MSF-BR system is the higher brine concentration, which increases the potential for having scale deposits on the heat transfer surfaces and for the liquid boiling point elevation (BPE), thus penalizing the coefficient of heat transfer and the available condensing temperature difference, respectively.
Increasing the MSF unit production (for both new designs and operating units) can be carried out either by: i) increasing the re-circulating brine flow rate, or ii) increasing the flashing range. Increasing the re-circulating brine flow rate is limited, however, by the available pump capacity and the chamber load (flashing brine flow velocity). Increasing the flashing range (TBT–BBT) can be carried out by increasing the top brine temperature (TBT), with hard-scale solution, or reducing the bottom brine temperature (BBT), with lower heat sink temperature (naturally in fall/winter/spring or utilizing deep intake or cooling towers). Increasing TBT is the parameter addressed in this paper.
At high TBT, scale deposits of high seawater brine concentration present a real problem in MSF plants, as they directly affect the heat transfer rates on the heating surface. The main scale-forming constituents are calcium (Ca++), magnesium (Mg++), bicarbonate (HCO3-), and sulphate (SO4--) ions. On heating, bicarbonate decomposes into carbonate CO3-, which reacts with Ca++ forming calcium carbonate (CaCO3) that precipitates on the heat transfer surface (if saturation limits are exceeded). At high temperature, magnesium hydroxide (MgOH) will also be formed. At higher temperature of >120°C, non-alkaline calcium sulphate (CaSO4) precipitates if saturation limits are also exceeded, due to inverse solubility. Formation of alkaline scale (CaCO3 and MgOH) can be controlled by lowering the pH (acid additives) or by anti-scalant. Non-alkaline (hard) scale (such as CaSO4) is only controlled nowadays by limiting the TBT below 120°C.
Scale deposits have a direct influence on the thermal units\' performance and water cost. Sulphate scales are a result of the direct crystallization of anhydrite (CaSO4), hemihydrate (CaSO4 0.5H2O), or gypsum (CaSO4 2H2O) from seawater once their solubility limits are exceeded as shown Fig. 10 [29]. Most of the deposited calcium sulphate found in seawater desalination plants is in the form of hemi-hydrate. The sulphate minerals are insoluble in common chemicals, and their development inside a distiller should be avoided by all means.
Figure 10.
Phase diagram of CaSO4
Increasing the TBT with hard-scale solution can be carried out by: i) introducing high-temperature anti-scalant, and ii) reducing hard-scale ions to avoid it from reaching the saturation conditions. The first is not yet available through the use of nano-filtration (NF) membrane system for make-up feed water pretreatment.
The application of NF in seawater desalination has gained significant attention in the desalination industry due to the selective removal of divalent ions. The SWCC R&D team [30-32] carried out extensive experiments on an MSF test pilot unit with NF as the pretreatment. NF pressure was 24 bars, and its recovery ratio ranged from 60% to 65%. The total concentration of the sulphate and calcium ions of the brine recycle was at a TBT of 130°C, and the makeup entirely formed from NF permeate was below the solubility limits. This result indicated the possibility of operating the MSF plant safely and without any scaling problem at TBT equal to or higher than 130°C. However, many questions on the adding of capital cost which might result in saving in operational cost still need clear answers.
The NF was originally applied to reject electrolytes and obtain ultra-pure water with high volume flux at low operating pressure, as most membranes have either positive or negative charge due to their compositions [33]. The NF membrane possesses a molecular weight cut-off of about hundreds to a few thousands, which is intermediate between reverse osmosis (RO) membranes and ultra-filtration (UF). The pore radii and fixed charge density of practical membranes were evaluated from permeation experiments of different neutral solutes of sodium chloride. The pore radii of these NF membranes were estimated to range from 0.4 to 0.8 nm [33].
The flexible and powerful tool ‘’Visual Design and Simulation program (VDS)’’ is used to perform process and techno-economical calculations. VDS was developed for the design and simulation of different types and configurations of the desalination processes [21-25]. Typical desalination processes are simulated to show the wide scope and high capability of the developed package. The description of the VDS software and discussions on how to access and handle the package are presented in [21-25]. In this work, the scope of the VDS program will be extended to develop and build up an NF system and a new MSF configuration model. The NF system’s mathematical model will be verified using typical NF-RO plant data.
Table (2) shows the CAPEX cost analysis of the NF system, which produces 226 m3/hr. The direct costs of the purchased equipment (membrane section, filters, pumps, valves, and piping) are included. The indirect costs of the building structure, engineering, and project development are also included. The intake cost is not included and is assumed to be included in the MSF CAPEX cost. The levelized cost is calculated (based on the 7% interest rate and 15 year life span) as 0.0775 $/m3 of the NF permeate as shown in column three of Table (2).
Table (3) shows the operational cost of the NF system, which includes labor, O&M, NF membrane replacement, electricity, and chemicals. The analysis showed that the cost of electricity represents the biggest chunk of the total OPEX, and the specific operational cost is 0.0566 $/m3 of the NF permeate. From both Table (2) and Table (3), the calculated unit permeate cost is 0.134 $/m3.
Figure 11 shows the interface of the existing 5,000 m3/day MSF-BR desalination plant at TBT=110°C [14]. The evaporator consists of 20 stages – 17 for the heat recovery section and 3 stages for the heat rejection section. The extracted steam from the power side is directed to the brine heater as a heat source. Sea water flows through the tubes of the heat rejection section condensers as a coolant. Part of this coolant outlet is used as a make-up, and the remaining coolant is rejected back to the sea. The make-up is directed to the de-aerator, and pretreatment chemicals are added, then mixed with a portion of the last-stage brine. The circulation pump circulates the diluted mixed brine to the condensers of the heat recovery section. The tube materials used in this plant are CuNi 90/10 for the brine heater and heat recovery section and CuNi 70/30 for the heat rejection section. The evaporator length is 29 m, the width is 7 m, and the height is 2.5 m. The design conditions are 27°C for seawater, and the brine velocity inside the tube is 2 m/s. The working pressure of the de-aerator is 0.055 bars, which is lower than the make-up saturation temperature of 38°C.
Figure 11.
Interface of the existing MSF-BR desalination plant at TBT=110 C [14]
Figure 12.
Interface of the NF-MSF-BR desalination plant [14]
Figure 12 shows the interface the MSF-BR with the NF system, which allows increasing the TBT to 130°C. The NF system treats one-third of the make-up. The feed of the NF system is extracted from the cooling reject stream (48 g/l) as shown in Figure (5). The NF permeate is mixed with the remaining make-up and directed to the de-aerator. The mixed make-up of low salinity of 43 g/l (15 % les) flows to the last stage of the heat rejection section. Due to the increase in the TBT from 110°C to 130°C, the distillate production increases by 19%. There is no increase of the GOR, as the heating steam increased also by 19%.
Table (4) shows that the CAPEX of the NF-MSF-BR system is 65.5% higher than that for the conventional MSF. Table (5) shows that the operating cost of the NF-MSF-BR system also increased by 22.4% higher than that for the conventional MSF.
Table (6) shows that the levelized CAPEX cost of MSF-BR at TBT=130°C is 16% lower than that for the conventional MSF at TBT=110°C. This is due to the increase in distillate production of 19%. Also, due to the increase in the productivity, the specific OPEX reduced by 2.5%. However, due to adding the NF system, the levelized OPEX of NF-MSF at TBT=130°C is 2.65% higher, while the specific CAPEX of NF-MSF is 28.7% higher than that for the conventional MSF.
The unit product cost of NF-MSF is 5.4% higher than that of the MSF plant. The analysis of these CAPEX and OPEX results shows that the OPEX cost has significant effect on the total unit water cost. This can be concluded that adding the NF system to an existing MSF plant (just to increase the production) is not enough to reduce the unit product cost.
A modified MSF-DM configuration has been proposed as shown in Figure 13. In this MSF-DM configuration, the heat rejection section is removed, and the bottom part of the de-aerator is utilized as a mixer where part of the last stage brine is mixed with de-aerated make-up. The new configuration is half-way between brine recirculation MSF-BR and once through MSF-OT and will benefit from both techniques and overcome the limitation encountered through operation. The GOR of the MSF-DM configuration at TBT=110°C could be as high as 12.
The MSF-DM design configuration is targeting high MSF GOR to be adopted in solar energy applications (high GOR is also needed, as the cost of energy is increasing). As the capital cost in solar energy systems is expensive, it will be cost-effective to develop high-performance MSF to reduce the CAPEX of the solar energy systems. A high-performance MSF system requires a combination of more evaporating stages, and more heat transfer surface area sequentially increases the MSF CAPEX. The increase in the MSF CAPEX could be balanced by reducing the MSF OPEX, and accordingly, CAPEX reduction of the solar energy system will be the main contribution to the developed system.
Figure 13.
The interface of the new MSF-DM for desalination plant [14]
Figure 14.
NF-MSF-DM configuration
Figure 14 shows the configuration of NF with the newly developed de-aeration brine mix NF-MSF-DM system to reduce the operational cost (OPEX). NF enables increasing the TBT to 130°C, while the MSF-DM enables increasing the GOR. As shown in Figure 14, the stage number of MSF-DM increased to 35, which is 75% higher than that of the conventional MSF-BR. The 61.5% of the last-stage brine is mixed with the de-aerated make-up flow of 675 m3/hr. The make-up is diluted from 48 g/l to 43 g/l using NF system permeate of TDS=28 g/l. This mixed is directed to the MSF condensers at 32.8°C, which is 15% lower than that for the conventional MSF (38°C). This lower temperature of coolant enhances the heat transfer process (condensation). However, the reducing cooling water reduces the LMTD across condenser compared with that of the conventional one. This explains why the heating surface area of MSF-DM was increased by 72%. One feature of increasing the heat transfer area of the heat recovery section is reducing the temperature difference across the brine heater, which sequentially increases the brine heater surface area. Increasing the heat transfer area of the heat recovery section increases the recovered energy, thus minimizing the external source of heating. Reducing the source of heating (steam) for fixed capacity will increase the GOR. The process calculations show that the GOR is 100% higher than that of MSF-BR (see Table (7)). This means that steam consumption is reduced by 100 %.
Table (7) shows the process calculation of MSF-DM at TBT=130°C compared with the conventional MSF at TBT=110°C. The GOR of MSF-DM-NF is twice of the conventional MSF; however, the heat transfer area is increased by 72%. Table (7) and Figure 14 show that the intake seawater of MSF-DM is 42% lower than that of MSF-BR. This, in turn, would reduce the seawater supply pump capacity, as well as the intake civil work. One feature of MSF-DM, the make is the same value of the conventional, which leads to having the same chemical cost of treatment and same manufacturing cost of de-aeration.
Table (7) shows that the specific power consumption of MSF-DM is 27% higher than that of MSF-BR. This is because of the increase of the friction loss due to the increase of the stage number by 75%. The evaporator length is increased by 142% in the case of MSF-DM; the evaporator width is decreased by 2%, while height is increased by 7% as shown in Table (7).
The purchased equipment cost (PEC) of these components is estimated based on recent market prices. In cases when data about the real installation cost of the desalination plant are scarce, the PEC of the individual components could be calculated based on cost relations. These relations of estimating the capital and operating costs of the components, such as pumps, valves, piping, and instrumentations are presented in [14].
A detailed cost breakdown is shown in Table (8). The evaporator (shell and tubes, de-aerator) cost of MSF-DM is 47% higher due to the increase in the heat surface area by 75% as shown in Table (7). Evaporator manufacturing cost, including the labor cost, of MSF-DM is 52% higher than that of MSF-BR. The costs of pumps, piping, valves, and I&C control of MSF-DM are lower than that of the conventional system due to the removal of the heat rejection section. The cost analysis shows that the intake construction cost of MSF-DM is 42% lower than that of the conventional one due to lower seawater flow rate. So the increase of MSF-DM evaporator cost is partially compensated by the cost reduction in auxiliaries and intake cost. The total capital cost (CAPEX) of the proposed configuration, MSF-DM, is 6% higher than that of the conventional MSF-BR. However, the total CAPEX cost of the NF-MSF-DM system is 71% higher than that of the conventional MSF. The main increase in CAPEX is contributed to the additional NF system.
Table (9) shows the OPEX items for both the conventional MSF-BR and the MSF-DM configurations. The cost of the steam and electricity is calculated based on an average of 80 $/barrel oil price and the recent purchase cost of power generation cycle [14]. The cost of the low-pressure steam is directed to the desalination plant, and the steam utilized for power generation is allocated based on exergy analysis [14]. Using levelization method through 20 years and 7%, the specific cost of low pressure steam is calculated as 7.5 $/m3 of steam, and the cost of the generated electricity is 0.043 $/kWh.
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\tItems\n\t\t\t
\n\t\t\t
\n\t\t\t\tMSF-BR (TBT=110)\n\t\t\t
\n\t\t\t
\n\t\t\t\tNF-MSF-DM (TBT=130)\n\t\t\t
\n\t\t\t
\n\t\t\t\t% diff\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
Evaporator
\n\t\t\t
1,066,100.45
\n\t\t\t
1,570,420
\n\t\t\t
47%
\n\t\t
\n\t\t
\n\t\t\t
Pumps
\n\t\t\t
306,223.35
\n\t\t\t
246,014
\n\t\t\t
-20%
\n\t\t
\n\t\t
\n\t\t\t
Piping, valves, I&C
\n\t\t\t
302,666.77
\n\t\t\t
179,202
\n\t\t\t
-41%
\n\t\t
\n\t\t
\n\t\t\t
Intake
\n\t\t\t
394,560.00
\n\t\t\t
194,416
\n\t\t\t
-51%
\n\t\t
\n\t\t
\n\t\t\t
Total
\n\t\t\t
2,069,550.57
\n\t\t\t
2,190,052
\n\t\t\t
6%
\n\t\t
\n\t\t
\n\t\t\t
NF
\n\t\t\t
-
\n\t\t\t
1,339,020.42
\n\t\t\t
100%
\n\t\t
\n\t\t
\n\t\t\t
Total
\n\t\t\t
2,069,550.57
\n\t\t\t
3,529,072.713
\n\t\t\t
71%
\n\t\t
\n\t
Table 8.
CAPEX analysis of MSF and NF-MSF-DM configurations [14]
The OPEX cost analysis (Table (9)) shows that the cost for NF-MSF-DM is 31% lower than that for the conventional MSF. The reduction in OPEX contributed to the reduction of the heating steam cost due to higher GOR. The levelized cost showed that the unit product cost of NF-MSF-DM is 21% lower than that of the conventional MSF as shown in Table (10).
As shown in Table (9), the low-pressure steam cost for the MSF-DM configuration is 48% lower than that for the conventional MSF-BR, and the steam consumption of MSF-DM is 100% lower than that consumed by the conventional MSF-BR. This is mainly due to the different steam cost invoked from the power side, as the heat steam temperature is higher in MSF-DM (TBT=130). The electricity cost of the MSF-DM is 27% higher than that of the conventional MSF-BR due to higher pumping power of the same order. The chemical cost is only 2% higher than that for the conventional MSF-BR. This is mainly due to the increase of make-up to be treated. The total number of OPEX items in the proposed configuration, MSF-DM, is 33% lower than that in the conventional MSF-BR, mainly due to low amount of steam consumption.
The annual investment cost (fixed capital cost depreciation rate (FCCDR) per year) of each component in the desalination plant is calculated according to the following relation:
Annual Investment = CAPEX ×i×(1+i)n(1+i)n−1E27
\n\t\t\t\t
Using an interest rate, i, of 7% and number of amortization years, n, of 20 years: then, the operation and maintenance cost is calculated by multiplying the equipment purchase cost by a factor of the equipment cost index. The hourly cost ($/hr) of the desalination plant is calculated as follows:
hourly−CAPEX=Total annual investment365×24×0.9E28
\n\t\t\t\t
Similarly, the hourly OPEX is calculated as follows:
hourly−OPEX=LP steam +Electricity+ChemiclasE29
\n\t\t\t\t
Then the unit product cost of the desalted water is calculated as follows:
Unit product cost, $/m3=hourly_CAPEX+hourly_OPEXhourly_ProductE30
\n\t\t\t\t
The levelized cost of capital purchased components and operating invested (chemicals, steam, electricity, O&M) to produce water is calculated as shown in Table (10). The specific OPEX of the MSF-DM is 34% lower than that of the conventional MSF-BR. The specific CAPEX of the MSF-DM is 12% higher than that of the conventional MAF-BR. However, the sum of the total cost invested using the MSF-DM is 34% lower than that of the conventional MSF-BR. Due to adding of the NF system, the specific OPEX of NF-MSF-DM is 20% lower that of the conventional one, while the specific CAPEX increased by 84% as shown Table (10). The total unit product cost of NF-MSF-DM is 9.5% lower than that of the conventional MSF-BR.
Levelized cost of MSF and NF-MSF-DM configurations [14]
4.2. Hybrid FO-MSF
In this section, technical approach to consider the impact of TBT and varying FO recovery on the process performance is presented. The VDS software [18] will be used as a powerful simulation tool. In this program, a reference MSF plant of 16.2 MIGD working at TBT=111°C is simulated. The performance ratio, distillate production, concentration and flow rates, and temperatures of all streams are calculated. The software is adapted and developed to consider the FO membrane. The hybrid MSF-FO is simulated at fixed brine recycle flow rate and brine concentration (draw solution) and by varying the FO recovery ratio with the TBT. For a fixed performance ratio, the distillate of MSF (D) and the required heat transfer surface area (A) are calculated at different operating conditions. For comparison, the specific heat transfer area (SA) is calculated as:
SA=ADm2/MIGDE31
\n\t\t\t\t
For the same seawater and draw solution flow rate across the FO membrane, the permeate (Dm) and the membrane area (Am) are calculated at different recovery ratios. For comparison, the specific area of FO membrane (SA) is calculated as follows:
SA=AmDmm2/MIGDE32
\n\t\t\t\t
At certain FO recovery ratio, the reduction in the Ca+ ions in the MSF feed is calculated and compared to the reference MSF process, which was operated without the FO process. The potential of CaSO4 scale formation in the MSF feed after dilution is estimated at different TBTs (115-135°C) using the Skillman index.
Using VDS, all process stream characteristics are determined (mass, temperature, pressure, entropy, and rated cost), and the heat transfer surface area (number of tubes), evaporator size, internal dimensions, and pumps are sized. So, a detailed CAPEX analysis is performed and estimated. The VDS software calculates the heating steam consumption rate and the consumed chemicals (anti scales, anti-foam, and chlorination), as well as the pumping power (OPEX items). The price of electricity and heating steam is estimated and calculated as illustrated in [18]. Then the final tariff of water unit cost is obtained.
Figure 15 shows the reduction in Ca+ ions in the feed of MSF desalination system at different recovery ratios of the FO membrane system. The reduction of Ca ions increases as the FO recovery ratio increases. At 40% recovery ratio, the reduction in Ca ions is calculated as 20%.
Figure 16 shows that the FO membrane water flux decreases as a result of the increase in the FO recovery ratio. The membrane flux decreases at higher recovery ratio due to dilution of the draw solution, which decreases the osmotic pressure driving force.
Figure 17 shows that the specific membrane area increases as the recovery ratio increases; this is due to lower water flux per unit area at higher recovery ratio. The higher value of specific membrane area is reflected in higher capital cost.
Figure 15.
reduction in Ca+ ions in MSF feed after FO dilution
Figure 16.
FO membrane flux at FO membrane recovery ratio variation
Figure 17.
Membrane area variation with FO recovery ratio variation
Figure 18 shows the Skillman index (SI) at different TBTs and the variation of FO recovery ratio. The SI of calcium sulphate solubility in case of the reference MSF plant without FO operating at TBT=111°C is calculated as 1.33. As the calculated SI of traditional MSF is greater than 1, the precipitate of calcium sulphate occurs. However, in practical MSF plant anti-scalant is used to disperse the crystalized scale. The SI=1.33 is considered as the reference for comparison; the value above 1.33 indicates scale formation, while the lower value indicates safe operation. As shown in Figure 5, the SI at different TBTs decreases as the FO recovery ratio increases. This is due to the increase in the removal of divalent ions. Figure 5 shows that the Skillman index increases as TBT increases. The MSF can operate at TBT=135 safely without scale problems at an FO recovery ratio of 40%. MSF at TBT=130°C can operate safely at a recovery ratio of 35%. Also, the MSF at TBT=125°C can operate safely at a recovery ratio of 30%. The MSF can operate safely at TBT=120°C and FO recovery ratio of 25%, while the MSF can operate safely at TBT=115°C and FO recovery ratio of 20%.
For the same performance ratio of MSF (PR=9), the reduction in the specific heat transfer surface area of MSF is calculated at different TBTs and different FO recovery ratios as shown in Figure 6. This figure shows that the reduction in specific heat transfer of MSF increases as the TBT increases. The increase of TBT resulting in increase of the logarithmic mean temperature difference between hot and cold streams of MSF, in turn, reduces the heat transfer area. Figure 6 shows that the reduction in SA slightly increases with the increase of the FO recovery ratio.
Figure 18.
Skillman index at different MSF TBTs and different FO recovery ratios
Figure 19.
Reduction in the heat transfer area (CAPEX) at different FO recover ratios and TBTs
For the existing MSF plant, at TBT=130°C, the production will increase up to 30% as shown in Figure 19. The question is whether or not the existing material can withstand the 135°C temperature.
Figures 17, 18, and 19 indicate that it is beneficial to work at higher TBT to reduce the heat transfer area or to increase the production of the existing plant of MSF (CAPEX/OPEX reduction); however, this requires higher recovery ratio of the FO membrane system, which requires higher membrane area (CAPEX increase). So, an economical evaluation and compromise to reach the trade-off point is still required.
The existing capacity of water desalination plants in Qatar is approximately 1.5 Mm3/day. MSF represent the main technology in Qatar. The make-up of seawater feed is chemically treated (anti-scalant, anti-foulant, and sodium sulphate) before being introduced to the heat recovery section. The amount of make-up flow rate is 3 times of the water production capacity, which is 4.5 Mm3/day. As shown in Table (11), the chemical cost is 2.35 M$/year.
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\tChemical\n\t\t\t
\n\t\t\t
\n\t\t\t\tDosing rate, ppm\n\t\t\t
\n\t\t\t
\n\t\t\t\tConsumption, kg/day\n\t\t\t
\n\t\t\t
\n\t\t\t\t$/year\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
Anti-scalant
\n\t\t\t
2.5
\n\t\t\t
2.81E+03
\n\t\t\t
2.28E+06
\n\t\t
\n\t\t
\n\t\t\t
Anti-foam
\n\t\t\t
0.1
\n\t\t\t
1.35E+01
\n\t\t\t
3.08E+04
\n\t\t
\n\t\t
\n\t\t\t
Sodium sulfate
\n\t\t\t
0.5
\n\t\t\t
2.25E+02
\n\t\t\t
4.11E+04
\n\t\t
\n\t\t
\n\t\t\t
Total
\n\t\t\t
\n\t\t\t
\n\t\t\t
2.35E+06
\n\t\t
\n\t
Table 11.
Chemical cost analysis of thermal desalination plant
Thus, it can be concluded that the integrated FO as a pretreatment unit to the seawater feed to the existing MSF desalination plant in Qatar is technically visible in terms of production capacity increase and chemical consumption decrease. However, cost analysis is required to balance the OPEX reduction with the addition caped of the FO membrane unit. Integrating FO to the existing MSF and using the brine of the last stage as a draw solution at a recovery ratio of 35% reduce the Ca+ ions in the seawater feed by 20%, which enables increasing the TBT up to 130°C safely. The simulation results show that at TBT=130°C, the production of the existing MSF plant increases by 20%. The OPEX analysis showed that an amount of 2.3 M$/year of chemical cost can be saved if the FO is deployed to the existing MSF plant in Qatar. The trade-off point between the additional CAPEX of the FO membrane system and the savings in OPEX will be considered under different operating condition in the present work.
5. Experimental study of hybrid NF-MSF
The process design and simulation for the test pilot is developed to prepare specifications of different components. Some units are manufactured by an Egyptian contractor, while others are purchased from vendors. The site is prepared where civil work and foundation are constructed. The test pilot components are installed and assembled, and finally, individual commissioning for each component is carried out. The site is located at the “Wadi El-Natroun” remote area, which is almost 150 km south-west of Alexandria city (Egypt). The site belongs to Alexandria University.
Figure 20.
Basic flow diagram of CSP-NF-MSF-DBM pilot plant [13]
Figure 20 shows the pilot test of the solar energy and desalination units. The concentrated solar parabolic trough with thermal energy storage facility provides the necessary heating to generate the required steam of the MSF desalination unit. The system is also equipped with a backup boiler for steam compensation. Solar PV and wind turbine (not present in Figure 20) are installed and run separately. However, in this phase, diesel engine is used to provide the pump electricity until the match and synchronization between the PV and the wind turbine are finalized.
5.1. MSF desalination unit
The MSF pilot unit consists of 28 flashing chambers with 28 connected condensers as shown in Figures 21.a and 21.b. The stages are arranged in double deck to reduce the foot print. There are four sets; each set consists of 7 stages. MSF chambers are equipped with glass windows for monitoring of the flashing process. The shell material of MSF is fabricated from 2 mm-thick stainless steel 316L. The flash chamber is 0.5 m in length and 0.5 m in width, while the height is 1.0 m. The condenser tube is 8 mm in diameter, 6 m long, and made of stainless steel (0.7 mm thick). The number of tubes is 2 per condenser, which are arranged in multi-pass inside a 0.5 m shell length. The unit is manufactured in Egypt and assembled at the project site.
The orifice opening area is controlled using gate valve, which is located between the flash chambers. The inter-stage valves controls the inter-stage flow rates to guarantee the brine flashing at each stage. The splash plate is designed just above of the inlet opening to reduce the carry-over. A demister is placed near the vapor outlet vapor pipes to reject the brine carry-over before going to the condenser. The shells are insulated to minimize energy losses. In addition to the brine heater, different supporting systems are added including vacuum system and chemical injection systems. The vacuum system has control valves at each stage to adjust the venting rate of non-condensable gases (NCG) and the stage pressure.
Figure 21.
MSF desalination unit with double deck [13]
The MSF is the main subsystem where distillation is produced using the flashing process. Different instrumentations are installed to measure and record the temperatures, pressures, and flow rates as shown in Figure 20. In the heating section, steam input and output temperatures, in addition to pressure and flow, are measured using proper transducers. All chambers are equipped with temperature and pressure indicators. The first and last chambers are equipped with temperature transmitter (TT) and pressure transmitter (PT), and the two additional movable PT and TT are supplied to be inserted in the chambers of the operator choice. Input seawater flow and output brine and distilled water flow rates are measured using flow transmitters.
5.2. Concentrated solar power (CSP) system
Four modules of solar concentrator (parabolic trough) are purchased and assembled in series at the site of the project as shown in Figure 22. Each module is 3.6 m in length and 1.524 in width. The collector area per module is 5.6 m2, while the collector reflective area is 5 m2. The assembled collector length becomes 14.6 m, while the total area is 22.4 m2. The receiver absorptivity is 0.92, the mirror reflectivity is 0.91, while the receiver emittance is 0.23. The black-coated pipes are 1.0 inch in diameter and placed in 2.0-inch-diameter glass pipes to minimize convection losses. The concentrators have a tracking system and were placed east-west and facing south.
Figure 22.
Four modules of the concentrated solar collector in series [13]
The CSP system contains a steam generator to supply the MSF brine heater with the required heating steam. Thermal oil is circulated through the collecting pipes, gains the solar thermal energy, and flows through the steam generator and energy storage tank. The steam generator consists of shell and tube and has a separate vapor header. The shell diameter is 10 inches and is 2 m in length. The hot oil passes through tubes, while the water flows through the shell. The tube length is 4 m, and the diameter is 6 mm; the number of tubes is 24, which are arranged in two passes. The CSP system is instrumented with temperature transmitters (TT), flow meters (FT), and pressure transmitters (PT), as shown in Figure 20, to monitor the temperatures, flow rates, and pressure in both steam and oil loops.
5.3. NF pretreatment
Figure 23.a shows the P&I diagram of the NF system. The system consists of dual media filter, cartridge filter, high-pressure pumps, chemical injection pumps, and nano-filtration (NF) membrane. One dual media filter vessel is installed with a specified feed flow rate of 1.5 ton/hr and 3.5 ton/hr for back wash. The vessel contains sand, gravel, and anthracite. The cartridge filter of 5 micron is installed after high pressure pump and just before the membrane section. The membrane section consists of 4 pressure vessels running in parallel; each vessel contains one membrane element of NF270 4040 type. The whole NF system, except feed, permeate, and brine tanks, is placed inside one container with its control panel, as shown in Figure 23.b. For water salinity, samples are collected periodically to measure the conductivity using a mobile conductivity meter.
Figure 23.
Nano-filtration (NF) system [13]
5.4. NF test performance
The NF system testing is carried out using the site brackish water (TDS=2000 ppm). A mathematical model of the NF membrane is developed and verified against typical operating NF unit data using the VDS software developed by the authors [13-15]. The VDS simulation results of the NF system were derived at different feed pressures of 8 and 10 bars and compared with experimental results as shown in Table (12). The NF performance was carried out and assessed by the recovery ratio and salt rejection. The recovery ratio (permeate/feed) increases as the feed pressure increases. The salt rejection (1- (permeate salinity/feed salinity)) is calculated as shown in Table (12). The salt rejection decreases as the feed pressure increases due to the increase in permeate salinity. The measured recovery ratio is slightly lower than the simulation results, although the salt rejection determined in the experiment is lower than that of the simulation. The differences between the measured values of permeate flow, salinity, recovery ratio, salt rejection, and simulation results are within the acceptable range.
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t
\n\t\t\t\tVDS\n\t\t\t
\n\t\t\t
\n\t\t\t\tExp\n\t\t\t
\n\t\t\t
\n\t\t\t\t% diff\n\t\t\t
\n\t\t\t
\n\t\t\t\tVDS simulation\n\t\t\t
\n\t\t\t
\n\t\t\t\tExp\n\t\t\t
\n\t\t\t
\n\t\t\t\t% diff\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
Feed pressure, bar
\n\t\t\t
8
\n\t\t\t
\n\t\t\t
10
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
Feed flow rate, ton/hr
\n\t\t\t
1.325
\n\t\t\t
\n\t\t\t
1.375
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
Feed salinity, ppm
\n\t\t\t
2000
\n\t\t\t
\n\t\t\t
2000
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
Permeate flow rate, ton/hr
\n\t\t\t
0.67
\n\t\t\t
0.6
\n\t\t\t
-10%
\n\t\t\t
0.85
\n\t\t\t
0.76
\n\t\t\t
-11%
\n\t\t
\n\t\t
\n\t\t\t
Permeate salinity, ppm
\n\t\t\t
648
\n\t\t\t
600
\n\t\t\t
-7%
\n\t\t\t
761
\n\t\t\t
650
\n\t\t\t
-15%
\n\t\t
\n\t\t
\n\t\t\t
Brine flow rate, ton/hr
\n\t\t\t
0.65
\n\t\t\t
0.725
\n\t\t\t
12%
\n\t\t\t
0.52
\n\t\t\t
0.6
\n\t\t\t
15%
\n\t\t
\n\t\t
\n\t\t\t
Brine salinity, ppm
\n\t\t\t
3395
\n\t\t\t
3158
\n\t\t\t
-7%
\n\t\t\t
4027
\n\t\t\t
3760
\n\t\t\t
-7%
\n\t\t
\n\t\t
\n\t\t\t
Recovery ratio, %
\n\t\t\t
51
\n\t\t\t
45
\n\t\t\t
-12%
\n\t\t\t
62
\n\t\t\t
55
\n\t\t\t
-11%
\n\t\t
\n\t\t
\n\t\t\t
Salt rejection, %
\n\t\t\t
67.6
\n\t\t\t
70
\n\t\t\t
4%
\n\t\t\t
62
\n\t\t\t
68
\n\t\t\t
10%
\n\t\t
\n\t
Table 12.
Typical NF experimental results compared with the VDS results [13]
5.5. Concentrated solar power (CSP) test performance
The CPS system, including the solar collector and steam generator, is simulated using the VDS program. The mass and heat balance equations of the solar collector, steam generator, and pumps are developed. The oil and water thermo-physical property correlations at different temperatures are considered in the program. The characteristic surface of collector reflectivity, receiver emission and absorptivity, and glass tube material transmittance are specified in the VDS program. The specifications of the solar collector and steam generator are defined and fed to the program. The measured weather conditions (solar intensity, ambient temperature, and wind velocity) at each hour are fed to the program. The duration time starts at 7:00 AM and ends at 8:00 PM with 1 hour step.
Figure 24.
ADD CAPTION
Figure 24.a shows the interface of the VDS program results at 4:00 PM. The oil mass flow rate and the temperature at inlet and outlet for both the solar collector and steam generator are presented. The collected energy is transferred to the steam generator to generate 3.8 kg/hr of saturated steam at 113.8°C. The solar intensity (I) and calculated absorbed energy by the receiver are shown in Figure 24.b. The difference is noticeable at mid-day time.
Figure 25.
Oil temperature variation through CSP trough and steam generator [13]
Figure 25.a shows comparison between the VDS simulation and experimental results of oil temperature rise through the solar collector during day time. The oil temperature difference increases as the solar intensity increases, while the maximum difference at mid-day reached 25°C. Figure 25.b shows a comparison between the simulation and experimental results of the oil temperature drop in the steam generator unit. The maximum heat transfer occurs during mid-day, and the maximum temperature drop is 14°C. It is similarly noticed that at day time, the temperature drop in steam generator unit is less than the temperature rise in the solar collector. This means that part of the gained energy in the collector is absorbed in the steam generator, and the remaining is maintained with the outlet oil stream from the steam generator and comes back the collector. This explains the increase of oil temperature at the concentrated solar collector inlet at day time.
The CSP system average efficiency () is calculated as the average useful gained power/average solar input power:
ηCSP=m.Cp|oil(To,oil−Ti,oil)I×ACSPE33
\n\t\t\t\t
Figure 26 shows the simulation and experimental results of the collector efficiency at day time. The collector efficiency decreases during day time due to the increase in the average oil temperature, which increases the energy loss to the ambient. The experimental collector efficiency shows relatively low value than that of the simulation collector efficiency due to: i) inaccurate tracking system that could not follow the sun movements accurately, and ii) the inefficient concentrated tube location in the CSP focus and possible convection loss.
Figure 27 shows comparison between the simulated and the measured generated steam temperatures. The water inlet and steam exit valve remain closed while the oil valves are open to allow energy transfer from oil to heat the enclosed water in the boiler. The water feed and steam valves are opened when the water temperature reaches 77°C. The generated steam temperature increases as the solar intensity increases, and the maximum temperature reached is 110°C at mid-day time.
Figure 26.
ADD CAPTION
Figure 27.
ADD CAPTION
Figure 28.
Generated steam flow rate [13]
Figure 29.
TBT variation [13]
The steam valve is opened at 1:00 PM at a steam flow rate of 4.3 kg/hr. The generated steam is directed to the MSF desalination unit as a heating source. The condensate steam in the brine heater of MSF is fed back to the steam generator. The amount of generated steam flow rate decreased linearly, as shown in Figure 28, due to the decrease in the solar collector efficiency. The measured generated steam flow rate shows lower values than the simulation results due to the thermal losses encountered through insufficient insulation of steam generator and throughout the connection pipe between the CSP outlet and steam generator. As shown in Figure 28, the operation of the steam generation extends up to 11:00 PM due to the heat storage in the CSP system.
Figure 29 shows the simulation and experimental values of TBT variation during day time. As the CSP steam condenses in the brine heater of MSF, the TBT rises up due to the gained energy of the latent heat. Under the ambient and operating condition in June 2012, the midday TBT reaches up to 100°C while the CSP steam condenses at 106°C, that is, 6°C temperature difference is maintained.
5.6. New MSF with de-aerator and brine mix (DBM)
The permeate water of the NF system is directed to the de-aeration and brine mix tower, where the feed is sprayed for oxygen removal. The deaerated water is mixed with parts of the brine blow down, then it is pumped to the MSF condensers. The brine mix feed absorbs latent heat energy in condensers before passing though the brine heater where the brine reaches its top temperature (TBT). The brine is then directed to the first flash chamber where flashing process occurs and vapor releases. The released vapor condenses to form product water. The flashing process occurs in the successive stages until the last stage is reached, where the un-flashed brine exits as brine blown down. The condensate of all stages is collected and directed to the water product tank. The brine level is adjusted above the interconnecting pipes (inter-stage gates) to guarantee the sealing of the flash chambers.
Under the same feed saline water flow rate (NF permeate) of 370 kg/hr and feed temperature of 27°C and controlling the brine mix ratio at 20-70% of the MSF brine blow down, the distillate water is measured and recorded at different TBTs, as shown in Figure 30, as compared with design calculated values. The pressure of saline water before the first chamber is controlled and fixed at an absolute value of 1.5 bars (above saturation conditions) by partially closing the valve. Also, the orifices among chambers are controlled by partially closing the valve between the two successive chambers. The in-tube water velocity is controlled at 2 m/s.
Figure 30.
MSF distillate productivity with TBT variation [13]
The rates of both the design and the measured distilled water increase as a result of the TBT increases as shown in Figure 30. The amount of distillate is lower than the expected; this may be due to the partial loss of flashed vapor through vacuum system and the irreversibility of the flashing process that occurs within the orifices and weirs.
Figure 31.
The GOR of MSF system variation with TBT [13]
Figure 31 shows the design and the experimental GOR of the MSF variation with TBT. This is defined as the ratio between the distillate flow rate and the heating steam consumption,. The average value of the unit design GOR is 17, which is almost twice of the conventional MSF GOR. The average measured GOR is 15 as shown in Figure 31. The small difference between the measured and designed values of GOR is due to the lower distillate productivity under fixed amount of heating steam flow rate.
The MSF specific power consumption (SPC) is defined as the ratio between the pumping power consumption (kW) and the rate of water distillate (m3/hr),.
Figure 32.
Specific power consumption (SPC) of MSF with TBT variation [13]
Figure 32 shows that the SPC decreases as the TBT increases mainly due to the increases in water productivity. The experimental SPC is calculated based on the measured distillate flow rate and the rated power consumption. The experimental SPC is higher, however, than the design value mainly due to lower experimental distillate for the same saline water feed and may be due to the pressure drop in piping and valves that were not considered properly in the design stage. The SPC of the test pilot unit is relatively higher than that of the commercial value of large scale MSF desalination plant due to the very small test pilot unit productivity.
6. Conclusion
To date, commercially available hybrid desalination plants are of the simple non-integrated type. They may share common systems such as intake and outfall facilities, but otherwise, they run independently at the same site. Product water from the membrane and thermal systems are usually blended to international standards on water quality. One more step ahead this chapter addresses the role of using FO or NF as a pre-treated method to the existing thermal desalination plants. The target of this hybridization is to reduce divalent ions that cause hard-scale deposition at elevated temperatures. The separation of divalent ion enables increasing the desalination process temperature greater than 110°C, which consequently increases the plant performance, increases the productivity, and reduces chemical consumption.
Integrating the NF system with new (MSF-DM) configuration at TBT=130°C, the gain output ratio could be as high as 16, which is double of that for the conventional MSF-BR. The new NF-MSFDM configuration significantly reduces the unit’s input thermal energy to suit the use of (the relatively expensive) solar energy as a desalination plant driver.
Simulation results showed that integrating FO to the existing MSF and using the brine of the last stage as a draw solution at a recovery ratio of 35% reduce the Ca+ ions in the seawater feed by 20%, which enables increasing the TBT up to 130°C safely. The simulation results show that at TBT=130°C, the production of the existing MSF plant increases by 20%. The OPEX analysis showed that an amount of 2.3 M$/year of chemical cost can be saved if the FO is deployed to the existing MSF plant in Qatar.
The desalination pilot test is built to evaluate the performance of the novel de-aeration and brine mix (MSF-DBM) configuration at high TBT using the NF membrane. The capacity of the desalination pilot plant is 1.0 m3/day of water. Comparison between the simulation and the experimental results of the pilot unit subsystems is relatively satisfactory. The newly developed NF-MSF-DBM (de-aerator and brine mix) configuration is tested at TBT=100°C, and the GOR is calculated as 15, which is almost twice of the traditional MSF under the same operating conditions. Using the new high-performance NF-MSF-DBM and the unit’s input thermal energy, which make the integration with (the relatively expensive) RE as a desalination plant driver, is a viable option.
\n',keywords:"Desalination, Thermal, Membrane, Hybrid, Cost",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/48625.pdf",chapterXML:"https://mts.intechopen.com/source/xml/48625.xml",downloadPdfUrl:"/chapter/pdf-download/48625",previewPdfUrl:"/chapter/pdf-preview/48625",totalDownloads:1279,totalViews:370,totalCrossrefCites:0,totalDimensionsCites:1,hasAltmetrics:0,dateSubmitted:"October 18th 2014",dateReviewed:"February 9th 2015",datePrePublished:null,datePublished:"October 28th 2015",dateFinished:null,readingETA:"0",abstract:"Hybrid desalination technology is defined as any combination of thermal and membrane processes in seawater desalination systems. So far, the two technologies have evolved rather independently with some degree of competition. Traditionally, in co-generation market applications, thermal desalination has succeeded in establishing a stronghold where large capacities are needed, energy costs are low, and seawater quality is challenging. However, in recent years, membrane systems have also succeeded in grabbing a larger share of the world seawater desalination market, mainly as a result of progress made in membrane and energy recovery technologies. Realizing the potential benefits and challenges faced by both technologies on their own, designers have been looking for ways to synergize and combine the two technologies in optimum configurations, which promise to further reduce the total cost of seawater desalination.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/48625",risUrl:"/chapter/ris/48625",book:{slug:"desalination-updates"},signatures:"Abdel Nasser Mabrouk, Hassan Fath, Mohamed Darwish and\nHassan Abdulrahim",authors:[{id:"173603",title:"Dr.",name:"Hassan",middleName:null,surname:"Abdulrahim",fullName:"Hassan Abdulrahim",slug:"hassan-abdulrahim",email:"habdelrehem@qf.org.qa",position:null,institution:{name:"Qatar Foundation",institutionURL:null,country:{name:"Qatar"}}},{id:"173604",title:"Prof.",name:"Mohamed",middleName:null,surname:"Darwish",fullName:"Mohamed Darwish",slug:"mohamed-darwish",email:"madarwish@qf.org.qa",position:null,institution:null},{id:"173774",title:"Dr.",name:"Abdel Nasser",middleName:null,surname:"Mabrouk",fullName:"Abdel Nasser Mabrouk",slug:"abdel-nasser-mabrouk",email:"aaboukhlewa@qf.org.qa",position:null,institution:{name:"Qatar Environment and Energy Research Institute",institutionURL:null,country:{name:"Qatar"}}},{id:"173942",title:"Prof.",name:"Hassan",middleName:null,surname:"Fath",fullName:"Hassan Fath",slug:"hassan-fath",email:"hfath@aus.edu",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_1_2",title:"1.1. Hybrid desalination concept",level:"2"},{id:"sec_2_2",title:"1.2. NF’s role in desalination",level:"2"},{id:"sec_3_2",title:"1.3. FO role in desalination",level:"2"},{id:"sec_4_2",title:"1.4. Objective",level:"2"},{id:"sec_6",title:"2. Process description",level:"1"},{id:"sec_6_2",title:"2.1. MSF-RO hybrid",level:"2"},{id:"sec_7_2",title:"2.2. NF-MSF process",level:"2"},{id:"sec_8_2",title:"2.3. FO-MSF",level:"2"},{id:"sec_9_2",title:"2.4. FO-MED",level:"2"},{id:"sec_11",title:"3. Methodology",level:"1"},{id:"sec_11_2",title:"3.1. Mathematical model development of NF",level:"2"},{id:"sec_12_2",title:"3.2. Mathematical model of forward osmosis (FO)",level:"2"},{id:"sec_14",title:"4. Technoeconomic analysis",level:"1"},{id:"sec_14_2",title:"4.1. NF-MSF",level:"2"},{id:"sec_15_2",title:"4.2. Hybrid FO-MSF",level:"2"},{id:"sec_17",title:"5. Experimental study of hybrid NF-MSF",level:"1"},{id:"sec_17_2",title:"5.1. MSF desalination unit",level:"2"},{id:"sec_18_2",title:"5.2. Concentrated solar power (CSP) system",level:"2"},{id:"sec_19_2",title:"5.3. NF pretreatment",level:"2"},{id:"sec_20_2",title:"5.4. NF test performance",level:"2"},{id:"sec_21_2",title:"5.5. Concentrated solar power (CSP) test performance",level:"2"},{id:"sec_22_2",title:"5.6. New MSF with de-aerator and brine mix (DBM)",level:"2"},{id:"sec_24",title:"6. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'K.P. Jong. Application of hybrid technology to the largest desalination plant, Fujairah, UAE, IDA World Congress, Bahamas (2003).'},{id:"B2",body:'H. Ludwig. Hybrid systems in seawater desalination, Desalination, 164 (2004) 1.'},{id:"B3",body:'Ata M. Hassan. Process for desalination of saline water especially water, having increased product yield and quality, Patent No. US 6,508,936 B1.'},{id:"B4",body:'Hassan Ata. 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Hybrid desalination systems, Middle East Desalination Research Center (MEDRC) Report (2000).'},{id:"B10",body:'O. Hamed. Overview of hybrid desalination systems, Desalination, 186 (2005) 207.'},{id:"B11",body:'Al-Mulla. Integrating hybrid systems with existing thermal desalination plants, Desalination, 174 (2005).'},{id:"B12",body:'P.K. Eriksson. Evaluation of nanofiltration as pretreatment to reverse osmosis in seawater desalination, IDA World Congress, Singapore (2005).'},{id:"B13",body:'Abdel Nasser Mabrouk and Hassan El-banna Fath. Experimental study of high performance hybrid NF-MSF desalination pilot test unit driven by renewable energy, Desalination and Water Treatment, 2103, DOI:10.1080/19443994.2013.773860.'},{id:"B14",body:'Abdel Nasser Mabrouk and Hassan El-banna Fath. Techno-economic analysis of hybrid high performance MSF desalination plant with NF membrane. Desalination and Water Treatment, 1944-3994/1944-3986@2012, http://dx.doi.org/10.1080/19443994.2012.714893.'},{id:"B15",body:'O. A. Hamed. Development of trihybrid NF/RO/MED desalination systems, Gulf water conference, Riyadh, 2007.'},{id:"B16",body:'S. Adham, R.C. Cheng, D.X. Vuong, K.L. Wattier. Long Beach’s dual-stage NF beats single stage SWRO, Desalination and Water Reuse, 13 (2003), 18.'},{id:"B17",body:'Ali Altaee, Abdel Nasser Mabrouk, Karim Borouni. A novel forward osmosis membrane pretreatment of seawater for thermal desalination processes. Desalination, 326, 19–26, October (2013). http://dx.doi.org/10/1016/j.desal.2013.07.008. (ISSN: 00119164).'},{id:"B18",body:'Ali Altaee, Abdel Nasser Mabrouk, Karim Borouni. Forward osmosis pretreatment of seawater to thermal desalination: High temperature FO-MSF/MED Hybrid System. Desalination, 339, (2014), 18-25. http://ex.doi/10.1016/j.desal.2014.02.006. (ISSN: 00119164).'},{id:"B19",body:'E. El-Sayed, M. Abdeljawad, S. Ebrahim, A. Al Saffar. Performance evaluation of two membrane configurations in a MSF/RO hybrid system, Desalination, 128 (2000) 231.'},{id:"B20",body:'Atta Hassan, M. Al Sofi, A. Al-Amoudi, A. Jamaluddin, A. Farooque, A. Rowaili, A. Dalvi, N. Kithar, G. Mustafa, I Al-Tisan. A new approach to membrane and thermal seawater desalination processes using nanofilteration membranes (Part I), Desalination, 118, 35–51 (1998).'},{id:"B21",body:'A. A. Mabrouk, A. S. Nafey, H. E. S. Fath. Thermoeconomic analysis of some existing desalination processes, Desalination, 205 (2007), 354–373. DOI: 10.1016/j.desal.2006.02.059, (ISSN: 00119164).'},{id:"B22",body:'A. A. Mabrouk, A. S. Nafey, H. E. S. Fath. Analysis of a new design of multi stage flash-mechanical vapor compression (MSF-MVC) desalination process, Desalination 204 (2007), 482–500. DOI: 10.1016/j.desal.2006.02.046, (ISSN: 00119164).'},{id:"B23",body:'A. S. Nafey, H. E. S. Fath, A. A. Mabrouk. Thermoeconomic investigation of multi effect evaporation (MEE) and hybrid multi effect evaporation-multi stage flash (MEE-MSF) systems, Desalination, 201 (2006), 241–254. DOI: 10.1016/j.desal.2005.09.044, (ISSN: 00119164).'},{id:"B24",body:'A. S. Nafey, H. E. S. Fath, A. A. Mabrouk. Exergy and thermoeconomic evaluation of MSF process using a new visual package, Desalination, 201 (2006), 224 –240. DOI: 10.1016/j.desal.2005.09.043, (ISSN: 00119164).'},{id:"B25",body:'A. S. Nafey, H. E. S. Fath, A. A. Mabrouk. A new visual package for design and simulation of desalination processes, Desalination, 194 (2006), 281–296. DOI: 10.1016/j.desal.2005.09.032, (ISSN: 00119164).'},{id:"B26",body:'Da Hee Jung, Jijung Lee, Do Yeon Kim, Young Geun Lee, Minkyu Park, Sangho Lee, Dae Ryook Yang, Joon Ha Kim. Simulation of forward osmosis membrane process: Effect of membrane orientation and flow direction of feed and draw solutions, Desalination, 277 (2011), 83–91.'},{id:"B27",body:'Tiraferri A., N. Yip, A. Straub, S. Castrillon. A method for the simultaneous determination of transport and structural parameters of forward osmosis membranes, J. of Membrane Science, 444 (2013), 523–538.'},{id:"B28",body:'M.A. Darwish, M.M. El-Refaee, M. Abdel-Jawad. Developments in the multi-stage flash desalting system, Desalination, 100 (1995), 35–64.'},{id:"B29",body:'Aiman E. Al-Rawajfeh, Hassan E.S. Fath, A.A. Mabrouk. Integrated salts precipitation and nano-filtration as pretreatment of multistage flash desalination system, Heat Transf. Eng., 33 (3) (2011), 272–279.'},{id:"B30",body:'Ata Hassan. Fully integrated NF-thermal seawater desalination process and equipment, US Patent No. 2006/0157410 A1, July 20, 2006.'},{id:"B31",body:'M. Al Sofi, Atta Hassan, G. Mustafa, A. Dalvi, N. Kithar. Nanofiltration as means of achieving higher TBT of >120°C in MSF, Desalination, 118 (1998), 123–129.'},{id:"B32",body:'Atta Hassan, A. Al Sofi, A. Al-Amoudi, A. Jamaluddin, A. Farooque, A. Rowaili, N. Dalvi, G. M. Kithar, I. Al- Tisan. A new approach to membrane and thermal seawater desalination processes using nanofilteration membranes (Part I), Desalination, 118 (1998), 35–51.'},{id:"B33",body:'X. Wang, T. Tsuru, M. Togoh, S. Nakao, S. Kimura. Evaluation of pore structure and electrical properties of nano filtration membranes. J. Chem. Eng. Jpn, (1995), 186–192.'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Abdel Nasser Mabrouk",address:"aaboukhlewa@qf.org.qa, abdelnaser.mabrouk@suezuniv.edu.eg",affiliation:'
Qatar Environmental & Energy Research Institute, Qatar
Qatar Environmental & Energy Research Institute, Qatar
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\n
1. Introduction
\n
The time management is important part for tasks in real time operation of systems, automation systems, optimization in complex system, taking explicit consideration in time constraints, scheduling of tasks and operations, making with incomplete data, time management in different practical cases. The limits in time for taking appropriate decisions for management and control is a strong constraints for the implementation of autonomic functionalities as self-configuration, self-optimization, self-healing, self-protection in computer systems, transportation systems, distributed systems. Time is an important and expensive resource.
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The time management in financial domain is a prerequisite for high competitiveness and increase of the quality of the investment activities. It is the popular phrase that “time is money” and particularly the portfolio optimization targets its implementation in real cases. This research targets the identification of portfolio parameters, which are strongly influenced by time. We restrict our considerations only on portfolio optimization task and we identify cases, which are strongly influenced by time constraints. Thus, the portfolio optimization problem is discussed on position how the time can influence the portfolio characteristics and solutions. This chapter starts with description of the object “portfolio management” which provides the cases where time in explicit way influences the portfolio problem.
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2. Portfolio optimization problem
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The task, which is resolved by the portfolio optimization of financial resources, is related with maximization of the return and simultaneously minimization of the investment risk. The portfolio optimization can be applied also to assets, which belong to the stock markets, because the same valued characteristics are used for portfolio optimization. The goal of the portfolio problem is to share the amount of investments among a set of securities, which are chosen to enter into the portfolio. The portfolio goal is to allocate in optimal manner the parts of the investment for buying securities. The time management problem initially arises with its complexity on the stage of the portfolio definition. The investment procedure has to be implemented at time t0 (now). The assets’ characteristics can be evaluated for this time moment t0, Figure 1.
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Figure 1.
Time schedule of the portfolio investment.
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The portfolio management insists to make decision for buying (or selling) assets at the current time t0. Then after a period of time \n\n∆\nt\n>\n0\n\n at time moment \n\nT\n=\n\nt\n0\n\n+\n∆\nt\n\n the investor has to sell (or buy) the assets from the portfolio and must receive positive return
The value of the Receipt is defined in the future time T and the Expenditure—on the current time t0. The portfolio problem arises according to the difference of the time moment \n\n\nt\n0\n\n<\nT\n\n. The investment decisions are based on the assets’ characteristics for the moment t0, A(t0). But in time T these characteristics will be A(T) and in common case they will differ in values \n\nA\n\n\nt\n0\n\n\n≠\nA\n\nT\n\n\n. These differences strongly influence the portfolio return at time T. In general, the assets’ characteristics are the return and risk, \n\n\nA\ni\n\n\n\nt\n0\n\n\n=\n\nA\ni\n\n\n\n\nReturn\ni\n\n\n\nt\n0\n\n\n\n\n\nRisk\ni\n\n\n\nt\n0\n\n\n\n\n,\ni\n=\n1\n,\n…\n,\nN\n\n, N is the types of assets in the portfolio which are evaluated for the current time t0. But the portfolio return is evaluated at the end of the investment period T. Respectively, the assets’ characteristics at time T are different \n\n\nA\ni\n\n\nT\n\n=\n\nA\ni\n\n\n\n\nReturn\ni\n\n\nT\n\n\n\n\nRisk\ni\n\n\nT\n\n\n\n,\ni\n=\n1\n,\nN\n\n. Hence, the final portfolio returns from (1) becomes
Following (2) for the implementation of the portfolio investment, the investor has:
to choose the types and number of assets N, which will participate in the portfolio;
to assess the assets’ characteristics Riski(t0) and Returni(t0), i = 1,…, N at the current time t0;
to choose the duration ∆t of the investment, which defines the final investment time T;
to forecast the assets’ characteristics Riski(T) and Returni(T), i = 1,…, N for the end of the investment period T;
to define and solve the portfolio optimization problem which will give the relative weights wi, i = 1,…,N of the investment, allocated for buying (selling) asset i. The relative values of weights introduce the analytical constraint
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\n\n\n∑\n\ni\n=\n1\n\nN\n\n\nw\ni\n\n=\n1\n\nE3
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and wi are the solutions of the portfolio optimization problem. To move ahead about the time management problem and to recommend relations between t0, ∆t and T there is a need to analyze the character of the portfolio optimization problem.
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3. Modern Portfolio Theory
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The Modern Portfolio Theory (MPT) was quantitatively introduced from Markowitz, with his seminal work [1]. The problems, introduced for the portfolio optimization are defined with two formal descriptions:
maximization of portfolio Return by finding optimal values of the assets’ weights wi, i = 1,…,N, satisfying constraints about portfolio Risk to stay below a predefined value
and/or minimization of portfolio Risk by finding optimal assets’ weights wi, i = 1,…,N, satisfying constraints about the portfolio Return to stay over a predefined value
Ei—the mean return of asset i = 1,…,N, ET = (E1, …, EN),
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∑ − is the covariance matrix of the assets’ returns, square symmetrical N × N matrix,
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\n\n\n\nσ\nmax\n2\n\n\n—the maximal portfolio risk, which the investor can afford for problem (4),
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Emin—the minimal portfolio return which the investor expects from the investment,
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wT = (w1, …, wN)—a vector of relative weights of the investment, which will be allocated to asset i = 1,…,N, for buying or selling.
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Particularly, additional nonnegative constraints are aided, wi\n\n≥\n\n 0, i = 1,…,N, which means that asset i will be bought for the portfolio. The case with negative weights, wi\n\n<\n\n 0 means that the investor will sell asset i at time t0 and at the end of the investment period T the will buy these assets to recover his wealth. During these operations the investor has to achieve positive portfolio return. The case of portfolio optimization with negative weights is named “short sells” but it is allowed only for special types of investors [2]. That’s the reason that MPT mainly applies an additional constraint for nonnegative weights w\n\n≥\n\n0 to problems (4) and (5).
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To be able to solve problems (4) and (5) the parameters E and ∑ have to be numerically evaluated. These parameters are strongly influenced by time. The estimation of the mean assets’ returns Ei, i = 1,…,N, has to be made for historical period. The portfolio manager must use a time series of assets’ returns
where \n\n\nR\ni\n\nm\n\n\n\n is the return of asset i at time m, i = 1,…,N, m = 1,…,n; n-discrete points from the return history. These return values could be on daily, monthly, weekly basis for a past period of time. Because for that case the time is defined as integer number of days/months/weeks, the number n describes the length of the historical period, taken by the portfolio manager to estimate the mean assets’ returns Ei, 1,…,N. The value of n is a discrete time and it influences the values of the assets’ characteristics. For a discrete time diapason 1\n\n÷\n\nn the mean assets’ returns are
The covariance coefficient cij has meaning, which defines how the time series of the assets’ returns i and j behave. The case of positive correlation cij\n\n>\n\n 0 means that if the time series of returns Ri of asset increase (or decrease) the same simultaneous change of increase (or decrease) takes place for the time series of returns Rj. For the case of negative correlation cij\n\n<\n\n 0, the time series Ri and Rj move in opposite directions. If the time series Ri increase (or decrease) the time series Rj decrease (or increase). The negative correlation has advantage in usage by the portfolio managers to decrease the total risk of the portfolio. Because cij = cji from (8), the covariance matrix ∑ is symmetrical. For the case i = j the value cii is the variation of the row Ri, \n\n\nc\nii\n\n=\n\nσ\ni\n2\n\n\n, \n\n\nσ\ni\n\n\n—standard deviation of row Ri. Thus, the covariance matrix on its diagonal gives the variation of the assets’ returns. The components cij define the behavior of the time series of returns Ri and Rm. The portfolio theory applies the variation \n\n\nσ\ni\n2\n\n\n as quantitative values of the risk of asset i. The graphical interpretation of mean return and risk of asset i is given in Figure 2, where.
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Figure 2.
Graphical interpretation of the risk and mean return of asset.
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Ri is the dynamically changed return of asset i,
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Ei—the mean value of return for the time period [t1, t2],
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\n\n\n\nσ\ni\n\n\n—standard deviation of Ri towards Ei and give value of the risk of asset i.
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The risk of the asset graphically represents the diapason [\n\n+\n\nσ\ni\n\n,\n−\n\nσ\ni\n\n\n] between which the real asset returns Ri generally stay around the mean value Ei. After definition of the vector of mean assets’ returns ET = (E1, …, EN) and the covariance matrix COV(.) = ∑, the portfolio return Ep analytically is evaluated as
The value of \n\nΨ\n\n is the “risk aversion” coefficient, which is normalized for the numerical diapason [0, 1].
For the case \n\nΨ\n=\n0\n\n the investor doesn’t care about the portfolio return and his goal is to achieve minimal portfolio risk.
For the case \n\nΨ\n=\n1\n\n the investor targets maximization of the portfolio return without considering the portfolio risk, because\n\nmin\n\n\n−\nΨ\n\nE\nT\n\nw\n\n\n≡\nmax\n\n\n+\nΨ\n\nE\nT\n\nw\n\n\n\n.
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By changing \n\nΨ\n∈\n\n0\n1\n\n\n different solutions \n\n\nw\nopt\n\n\nΨ\n\n\n are found from problem (11) which gives corresponding returns \n\n\nE\np\n\n=\n\nE\nT\n\n\nw\nopt\n\n\nΨ\n\n\n and risk \n\n\nσ\np\n2\n\n=\n\nw\n\no\npt\n\nT\n\n\n\nΨ\n\n∑\n\nw\nopt\n\n\nΨ\n\n\n for the portfolios. These set of solutions can be presented as a set of points [\n\n\nσ\np\n2\n\n,\n\nE\np\n\n\n] in this space which in continuous case origins the “efficient frontier” curve, Figure 3.
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Figure 3.
The curve of “efficient frontier” and the market point.
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The efficient frontier has quadratic character but it is not a smooth line [3]. This non-smooth character origins from the existence of non-negative constraints wi\n\n≥\n0\n\n, i = 1,…,N in problem (11). Hence, the MPT recommends to be defined and solved portfolio problem (11). Because the investors have different ability to undertake risk, the portfolio manager has to estimate the correct value of the “risk aversion” parameter. Because such identification is strongly subjective influenced, the MPT recommends to be evaluated the “efficient frontier” of portfolios. The investor can choose appropriate point from the frontier, which corresponds to the relation Risk/Return, which the investor is willing to accept. The portfolio, applied in problem (11) is named also “mean-variance” (MV) portfolio model. From the time management considerations, the cases which are influenced by the time, for the portfolio problems are summarized as:
the portfolio manager has to choose the time for the portfolio implementation;
he has to decide the duration of the investment ∆t = T–\n\n\nt\n0\n\n\n; T—final investment time;
he has to choose the duration n of the historical period, which will be used for the evaluation of the mean assets’ returns Ei, i = 1, N and the covariance matrix COV(.) = ∑ of the assets’ returns. The diagonal values of matrix ∑ gives assets’ risks \n\n\nσ\ni\n2\n\n,\ni\n=\n1\n,\n…\n,\nN\n.\n\n
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Thus, the time is very important parameter, which influences the definition and implementation of the portfolio investment and optimization.
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4. Capital Market Theory
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The MPT originated by the works of Markowitz has its further developments. The next important stage of MPT is the definition of the Capital Market Theory, [2]. The Capital Market Theory introduces a new point on the “efficient frontier,” named “market portfolio.” It has analogical portfolio characteristics as market return \n\n\nE\nM\n\n\n and market risk \n\n\nσ\nM\n2\n\n\n. This theory derives new analytical relations with the market characteristics, which are formal part of the Capital Asset Price Model (CAPM). This model added three additional linear relations named Capital Market Line (CML), Security Market Line (SML) and cHaracteristic Line (HL).
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The graphical representation of the CML is given in Figure 3. It starts from the point (0,\n\n\n\nr\nf\n\n\n) which is a riskless asset with mean return \n\n\nr\nf\n\n\n. The market point \n\n(\n\nE\nM\n\n,\n\nσ\nM\n2\n\n)\n\n is a tangent one over the “efficient frontier.” The CML gives relations between the portfolios returns and risks for a particular market, assessed by the characteristics \n\n\nr\nf\n\n,\n\nE\nM\n\n,\n\nσ\nM\n2\n\n\n. Analytically, the CML is a linear relation between \n\n\nE\np\n\n\n\nand \n\n\nσ\np\n\n\n,
By estimating the market parameters \n\n\nr\nf\n\n,\n\nE\nM\n\n,\n\nσ\nM\n2\n\n\n the investor has information about the level of risk \n\n\nσ\np\n2\n\n\n, which has to be undertaken by means to obtain portfolio return \n\n\nE\np\n\n\n. This prevents the investor to have unrealistic expectation about the potential mean return, which has to be achieved by a portfolio. The values of the market parameters,\n\n\n\nE\nM\n\n,\n\nσ\nM\n2\n\n\n are defined mainly according to the behavior of market index (S&P500, Dow Jones Industrial Average, NASDAQ Composite, NYSE Composite, FTSF100, Nikkei225, IPC Mexico, EURONEXT 100 and others). On each market the risk-free assets (deposits, long time bonds) has its own value \n\n\nr\nf\n\n\n.
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The SML introduces linear relations between the mean return of a particular asset \n\n\nE\ni\n\n\n and the market return \n\n\nE\nM\n\n\n
The “beta” coefficient takes normalized values from the diapason [−1, 1]. Numerically, it defines how strong the mean return value \n\n\nE\ni\n\n\n is related with the market return \n\n\nE\nM\n\n\n. If the return \n\n\nE\ni\n\n\n is strongly related to the market behavior, the coefficient \n\n\nβ\ni\n\n\n has high value, close to 1, if the covariation coefficient cov(i,M) is positive. The case of \n\n\nβ\ni\n\n<\n0\n\n means that the covariance between the series of returns Ri and RM are in opposite directions.
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The HL line makes additional clarification between the current value of the asset return Ri and market one RM
Relation (15) is timely influenced. If the market value RM is changed/predicted, the corresponding asset return Ri of asset i can be estimated and/or predicted.
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The CAPM does not apply explicit inclusion of time in its characteristics. Time explicitly influences only the values of the market return \n\n\nE\nM\n\n\n and market risk \n\n\nσ\nM\n\n\n. Applying the same considerations which take place for the evaluation of the assets’ characteristics Ei,\n\n\n\nσ\ni\n\n\ni = 1,…,N the historical period for the evaluation of the market characteristics is recommended to be the same, with n discrete historical values of the market return \n\n\nR\nM\n\n=\n\n\nR\nM\n\n1\n\n\n\nR\nM\n\n2\n\n\n…\n\nR\nM\n\nn\n\n\n\n\n.
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5. Black-Litterman model for estimation of portfolio characteristics
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The Black-Litterman (BL) model is based on both achievements of the MV portfolio model and CAPM. The idea behind the BL model is the ability to use additional information by means to estimate and to predict the assets’ characteristics Ei(T) and \n\n\nσ\ni\n\n\nT\n\n\n, i = 1,…,N [4, 5, 6]. The difference and the added value N for the future time moment T when the portfolio investment will be capitalized e of the BL model is graphically interpreted in Figure 4.
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Figure 4.
Additional modification of portfolio parameters by BL model.
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The MV model estimates the assets characteristics Ei, \n\n\nσ\ni\n\n\n, i = 1,…,N using historical data from n discrete points of the assets’ returns \n\n\nR\ni\n\nm\n\n\n,\ni\n=\n1\n,\n…\n,\nN\n,\nm\n=\n1\n,\n…\n,\nn\n\n. The BL model allows additional information to be used by means to modify the mean values of return ET = (E1, …, EN) as the assets’ risk characteristics, given by the covariation matrix ∑. The modification of ET to a new vector \n\n\nE\nBL\nT\n\n=\n\n\nE\n\nBL\n1\n\n\n…\n\nE\nBLN\n\n\n\n is made by two additional numerical matrices P and Q. These matrices are evaluated from expert views, who make a subjective assessment about the future levels of assets’ returns at time T, when the portfolio investment should be capitalized.
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P is a k×N matrix, which contains k expert views. The vector Q defines quantitative information about the k-th expert view for increase or decrease the mean return Ei of i-th asset. The elements pki of P defines the view of k-th expert about the change of the Ei return of asset i. The component pki takes value +1 for the case of increase, and respectively −1 for decrease.
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The BL model added a new contribution to the MPT by introducing new characteristic of the portfolio asset: “implied return,” \n\n\nП\ni\n\n,\ni\n=\n1\n,\n…\n,\nN\n\n (“implied excess return,” when the return is evaluated according to the level of risk-free asset \n\n\nr\nf\n\n\n). These returns differ from the historically evaluated mean returns Ei, i=\n\n1\n,\n…\n,\nN\n\n. The assumption behind these new “implied returns” is related with the existence of market point \n\n(\n\nE\nM\n\n,\n\nσ\nM\n\n\n). For the case of market equilibrium, the CAPM asserts that all assets, which participate on this market should have appropriate mean returns \n\n\nП\nТ\n\n=\n(\n\nП1, … ПN) and market weights \n\n\nw\nM\nT\n\n=\n(\n\nw\n\nM\n1\n\n\n\n,…, \n\n\nw\nMN\n\n\n). Hence from the market values \n\n(\n\nE\nM\n\n,\n\nσ\nM\n\n\n) it follows exact values of П and w. But the market is a stochastic system and it endues a lot of noises, which change the values of the “implied returns.” These returns \n\n\nП\ni\n\n,\ni\n=\n1\n,\n…\n,\nN\n\n\nare values, which “should be.” But the noises make changes to \n\n\nП\ni\n\n\n and the BL model evaluates the unknown mean values EBL which are the “best approximation to \n\n\nП\ni\n\n\n.” These considerations origin the matrix linear relation in BL model
where the noise \n\nε\n\n\nis assumed to be with normal distribution, zero mean and volatility proportionally decreased from the historical covariance matrix, \n\nε\n∼\nN\n\n0\n\nτ\nΣ\n\n\n\n, \n\n0\n<\nτ\n<\n1\n\n. The subjective views formally are introduced by the linear stochastic relation
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\n\nQ\n=\nP\n\n\nE\nBL\n\n+\nη\n,\n\nE17
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where Q is the quantitative assessment of the experts’ views about the value with which the historical returns will change; P identifies which assets’ returns will be changed. The expert views contain also noise \n\nη\n\n. Due to the independence of the expert views the noise \n\nη\n\n is assumed with zero mean and volatility \n\nΩ\n\n, \n\nη\n∼\nN\n\n0\nΩ\n\n\n. The matrix \n\nΩ\n\n is kxk square one with only diagonal elements because of the independence of the expert’s views. The matrix \n\nΩ\n\n is presented mainly in the form [7].
The goal of the BL model is the evaluation of the returns \n\n\nE\nBL\n\n\n which have to approximate in maximal level the stochastic relations (16) and (17). The values of the vectors and matrices П, Q, P, \n\nε\n\n, \n\nη\n\n are assumed to be known and/or estimated. The definitions of these parameters are given in the next paragraph.
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6. Definition of the “implied excess returns”
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Using [8, 9] the assumption is made that the “implied excess return” П must satisfy the market portfolio. The goal function of the portfolio problem for that case is
where \n\nλ\n=\n\n\n1\n−\nΨ\n\nΨ\n\n\n is not normalized value of the risk aversion coefficient, \n\nλ\n∈\n\n0\n∞\n\n\n. Because the market point is used in (18) according to the CAPM the relation \n\n\nw\nM\nT\n\n.\n1\n=\n1\n\n is satisfied, \n\n\n1\nT\n\n=\n\n1\n\n…\n1\n\n\n\n is a unity Nx1 vector. The unconstrained minimization of (19) gives solution
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\n\nλ\n∑\n\nw\nM\n\n−\nП\n=\n0\n.\n\nE20
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By multiplication from left of the both sides of (20) with market capitalization weights \n\n\nw\nM\nT\n\n\n it follows
The right component of (21) contains the market “excess return” \n\n\nE\nM\n\n−\n\nr\nf\n\n\n, according to (9). The left side gives the market volatility (risk) \n\n\nσ\nM\n2\n\n\n, (10) or
The “implied return” П* is the value of П to which the riskless return is added
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\n\n\nП\n∗\n\n=\nП\n+\n\nr\nf\n\n.\n\nE24
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This manner of definition of П is known as “inverse optimization” because the market risk and return are known, but we need to calculate the asset returns.
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7. Definition of P and Q from scientific views
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Following [10] absolute and relative manner for the formalization of the expert views are applied. The explanation of these forms of formalization is given with a simple example. Let’s the portfolio contains N = 4 assets. Assuming that an expert expects that the first asset will increase its return with 2%; a second expert makes conclusion that the fourth asset will decrease its return with 3% the formalization of P, Q are
The relative form of views applies comparisons between the assets’ returns. Let’s the first expert expects that the first asset will outperform the third one with 2.5%; the second expert makes view that the second asset will outperform the fourth one with 3.5%. The formalization of matrices P and Q are
The two types of formalization of expert views is widely mention in references dealing with the BL model [7, 10]. A new form of expert views has been developed in [11]. It has been applied a weighted form for the definition of matrix P, where its components can take values different from \n\n±\n1\n\n. To provide this new formalization of the expert views the matrix \n\nΩ\n\n is analyzed. This matrix formalizes the variation of the expert views. Using relation (18) let’s assume that the portfolio contains three assets, N = 3 and two experts k = 2 make views in relative form formalized in the matrices P and Q
where \n\n∑\n\n is a symmetrical 4 × 4 matrix \n\n\n\n\n\n\n\n\nσ\n1\n2\n\n\n\n\nσ\n12\n\n\n\n\n\n\n\n\n\nσ\n21\n\n\n\n\n\n\nσ\n31\n\n\n\n\n\n\nσ\n41\n\n\n\n\n\n\n\n\n\n\nσ\n2\n2\n\n\n\n\n\n\nσ\n32\n\n\n\n\n\n\nσ\n42\n\n\n\n\n\n\n\n\n\n\n\n\nσ\n13\n\n\n\n\nσ\n14\n\n\n\n\n\n\n\n\n\nσ\n23\n\n\n\n\n\n\nσ\n3\n2\n\n\n\n\n\n\nσ\n43\n\n\n\n\n\n\n\n\n\n\nσ\n24\n\n\n\n\n\n\nσ\n34\n\n\n\n\n\n\nσ\n4\n2\n\n\n\n\n\n\n\n\n\n\n. The matrix multiplications results in 2 × 2 matrix \n\nΩ\n=\n\n\n\n\n\nω\n1\n\n\n\n0\n\n\n\n\n0\n\n\n\nω\n2\n\n\n\n\n\n\n where
Relations (29) have analytical structure with the risk relation of portfolio with two assets, N = 2, and negative correlation, [2] \n\n\nσ\np\n2\n\n=\n\nw\n1\n2\n\n\n\nσ\n1\n2\n\n+\n\nw\n2\n2\n\n\n\nσ\n2\n2\n\n−\n2\n\nw\n1\n\n\n\nw\n2\n\n\n\nσ\n12\n\n\n where \n\n\nσ\n1\n2\n\n\n and \n\n\nσ\n2\n2\n\n\n are the volatilities of the two assets, \n\n\nσ\np\n2\n\n\n is the volatility of the portfolio, \n\n\nσ\n12\n\n\n is the covariation between the two returns. Assuming equal weights in the portfolio, \n\n\nw\n1\n\n=\n\nw\n2\n\n\n, the portfolio risk is evaluated as
The comparisons between relations (29) and (30) can be interpreted that in (29)\n\n\nω\n1\n\n\n and \n\n\nω\n2\n\n\n are the values of risks of two virtual portfolios. The first one contains assets one and three. The second portfolio has the second and fourth assets. Thus, the values \n\n\nω\ni\n\n\ni\n=\n1\n,\n2\n\n, which formalize the risk of expert views are proportional to virtual portfolios with corresponding two assets, which have negative correlations and equal weights.
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Now let’s assume that the matrix P contains weighted components \n\n\nα\ni\n\n\n, which differ from the values \n\n±\n1\n\n. To simplify the formal notations we assume that the matrix P is on the form.
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P =\n\n\n\n\n\n\n\n\n\nα\n1\n\n\n0\n−\n\nα\n3\n\n\n0\n\n\n\n\n\n0\n−\n\nα\n2\n\n\n0\n\n\nα\n4\n\n\n\n\n\n\n\n\n. The weighted coefficients satisfy the equalities
Relations (32) interpret that for the weighted form P(\n\nα\n\n) of the expert views the corresponding components \n\n\nω\ni\n\n\ni\n=\n1\n,\n2\n\n of the variation of the expert views are proportional to the risk of a portfolio with two assets and negative correlation, and the assets weights \n\nα\n\n are normalized because equalities (31) hold. The ability to define matrix P with components different to \n\n±\n1\n\n allows the expert views to be generated not only by subjective assessments, but also with additional considerations, which are based on objective criteria, estimations and assessments.
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This research makes several additions to the numerical definition of P and Q matrices.
1. Formalization P(\n\nα\n\n) based on the difference Пi–Ei, i = 1,…,N, normalized by the i-th volatility.
Following [11] a row of matrix P concerning the view of an expert is defined in the form \n\n\np\ns\n\n=\n\n\n0\n…\n\nα\ni\n\n\n0\n…\n0\n−\n\nα\nj\n\n…\n0\n\n\n\n, 1xN vector. The values \n\n\nα\ni\n\n\n and \n\n\nα\nj\n\n\n must satisfy the normalization equation \n\n\n\nα\ni\n\n\n+\n\n\nα\nj\n\n\n=\n1\n\n. The value \n\n\nα\ni\n\n\n is chosen from the maximal difference
Relation (33) presents that the mean history’ return of asset i, \n\n\nE\ni\n\n\n, is lower from its “implied excess return” and the investor has to expect that the return of asset i has to increase. The same considerations, but for decrease of the mean return \n\n\nE\nj\n\n\n is made from the difference
Asset j is over performed and the investor has to expect decrease of the historical mean return \n\n\nE\nj\n\n\n towards the level of the “implied excess return” \n\n\nП\nj\n\n\n.
4. A particular case can arise when all differences \n\n\nα\ni\n\n=\n\nПi–Ei, i = 1, N have equal sign (+) or (−). Hence all assets’ returns have to be increased, when \n\n\nα\ni\n\n>\n0\n\n or decreased if \n\n\nα\ni\n\n<\n0\n\n.
\n
For that case absolute views can be assign. The matrix P will be square NxN identity matrix. \n\n\n\n\n\n1\n\n\n…\n\n\n0\n\n\n\n\n⋯\n\n\n1\n\n\n…\n\n\n\n\n0\n\n\n…\n\n\n1\n\n\n\n\n\nN×N. The Q, N×1 vector will have components equal to \n\n\nα\ni\n\n=\n\nПi–Ei, i = 1,…,N.
\n
Thus, for the formalization of p. 2 the matrices P and Q are
for the case of p. 3. These four forms of weighted formalization of matrix P(\n\nα\n\n) allows to be overcome the need to have subjective expert views. With these formalizations the assets’ characteristics are evaluated not only by historical returns and covariances but by adding data, which in this case concerns differences from the “implied returns.” The |BL model incorporates such additional source of information, Figure 4. The formalism P(\n\nα\n\n) allows to be compared portfolio solutions, based on MV model and BL one because subjective influences in BL model now are missing. The BL model integrates different sources of information, concerning future assets’ characteristics, but this information is not subjectively generated and it origins from real and actual behavior of the market.
\n
\n
\n
8. BL modification of the assets’ characteristics
\n
Using relations (22) and (23) the BL returns EBL are found by means to approximate in best way these two linear stochastic relations. For simplicity additional notation are used in the next matrix relations
Using these modified assets’ characteristics, the portfolio problem (11) is solved and appropriate point from the efficient frontier is chosen. It is recommended the best portfolio to be taken with weights \n\n\nw\ni\nopt\n\n,\ni\n=\n1\n,\n…\n,\nN\n\n, which belongs to portfolios with characteristics
\n\nor maximal information ratio\n,\n\n\n\nmax\n\n\n\n\nw\n\n\n\n\n\n\n\nE\np\n\n\nσ\np\n\n\n\n\nE46
\n
\n
\n
9. Numerical simulations and comparisons between MV and BL portfolios solutions
\n
The numerical simulations are performed with real data from the Bulgarian Stock Exchange [12]. The riskless investment for several years gives very low or even negative return. That is, the reason for the investors to start to apply portfolio optimization with risky assets. Currently, the risky investments are performed with a set of about 125 mutual funds in Bulgaria nowadays. The mutual funds are operated by different business and economics entities. The goal of all mutual funds is to manage their portfolios by means to achieve positive return or to decrease the losses in nonfriendly behavior of the financial market. The success or not successful management of the mutual funds can be seen by their historical data about achieved returns and risks in their investments. Thus, our portfolio simulations will start with historical return data of a set of chosen Bulgarian mutual funds. It has been chosen seven mutual funds to participate in the portfolio: Concord Asset Management (CONCORD), Elana Asset Management (ELANA), Profit Asset Management (PROFIT), Texim (TEXIM), Central Cooperative Bank Lider (LIDER), Asset Management UBB Patrimonium (PATRIM), Asset Management DSK Growth (GROWTH). They invest both in currencies and shares. The Bulgarian Association of Asset Management Companies [13] and the Government Financial Supervision Commission [14] regularly record and update the activities of the Bulgarian mutual funds. For the simulation experiments it has been taken the mean monthly return of these 7 mutual funds for 2018-year, Figure 5.
\n
Figure 5.
Monthly and annual returns, and the covariance matrix of the mutual funds for 2018.
\n
The calculations in this research have been performed in MATLAB environment. The mean years returns and the covariance matrix are given also in Figure 5. The simulations apply multiperiod investment policy, described in Figure 6.
\n
Figure 6.
Multi period investment with flowing historical window.
\n
\n
9.1 Initial evaluation of historical data
\n
The monthly mean returns of the mutual funds for the first 8 months of 2018 were taken as historical period. It has been calculated the average return for each fund for this historical period, n = 8. The average returns and the corresponding covariance matrix are given in Figure 7.
\n
Figure 7.
Mean returns and covariance matrix for the first 8 months of 2018.
\n
The portfolio manager has to pay attention for the different values of mean returns and covariance, given in Figures 5 and 7. The first case is evaluated for n = 12, 12 time period. While the second evaluations are made for a shorter period, n = 8. That is, a case where the time management is important for the estimation of the assets’ characteristics.
\n
\n
\n
9.2 Evaluation of the efficient frontier with MV model for the first 8 months
\n
By changing the values of \n\nΨ\n∈\n\n0\n1\n\n\n the portfolio problem (11) is repeatedly solved. The interim values of the portfolio return, risk and portfolio weights are stored in working arrays in MATLAB environment. The evaluation step of changing \n\nΨ\n\n was chosen \n\nΨ\n=\n0.01\n\n resulting in 100 solutions of problem (11). The graphical presentation of the MV “efficient frontier” is given in Figure 8.
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Figure 8.
Graphical presentation of the “efficient frontier” with historical data.
\n
The Sharpe excess ratio (45) and the information ratio (46) are presented in Figure 9.
\n
Figure 9.
Graphical presentation of Sharpe excess ratio and information ratio.
\n
It is estimated the maximum Sharpe_excess_ratio = 4.321. This value corresponds to a portfolio with characteristics:
These results recommend that the portfolio manager has to allocate his investment only in two mutual funds: the second in the portfolio (ELANA) and the third one (PROFIT). This recommendation is valid for the investment month of September 2018.
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\n
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9.3 Evaluation of the assets’ characteristics for the BL model
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9.3.1 Definition of the risk-free return rf
\n
In this research for the risk-free return rf has been used an official index, evaluated and maintained by the National Bank of Bulgaria. The index is named LEONIA+ which is abbreviation of Lev (the name of the National currency) Over Night Index Average. This index is used by the mutual funds to take or giving loans for overnight activities on the financial market. This index is recommendation from the Bulgarian National Bank for all financial institution and authorities in Bulgaria dealing in overnight deposits with Bulgarian currency [15]. For this research the risk-free value is negative on monthly basis, rf = −0.4.
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\n
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9.3.2 Evaluation of the market point
\n
The characteristics of the market point are the mean return EM and the risk, numerically estimated by the standard deviation \n\n\nσ\nM\n\n\n. The market point is found as a tangent one where the CML (Capital Market Line) makes over the “efficient frontier.” Additionally, the CML must pass through the riskless point (0, rf). The CML cannot be presented in analytical way because the “efficient frontier” is not analytically given. The last have been found numerically as a set of points in the plane (Risk/Return) from the multiple solutions of portfolio problem (11), given in p. 2. This research makes a quadratic approximation of the “efficient frontier” and finds analytical description of the “approximated efficient frontier.” Then with algebraic calculations using the linear equation of the CML and the approximated efficient frontier the tangent point is evaluated. The coordinates of the market point give the mean market return EM and the market risk \n\n\nσ\nM\n\n\n. For these market values the market capitalization weights wM are found from the working arrays when problem (11) has been solved in p. 2. The “approximated efficient frontier” is a quadratic curve of the form
9.3.4 Definition of the characteristics of the expert views P and Q
\n
The portfolio parameter, which is used for the estimation of matrices P and Q is the difference between the implied returns П and the mean assets’ historical returns E, (П–Е). These values are as follows:
Because the value of the third component of (П*-E)T is less than 0.1% it is assumed to be zero. All differences (П*-E) have positive sign, which means that the assets are underestimated and their implied returns are higher. Hence, the portfolio manager has to expect an increase of the mean returns of the assets in the portfolio. This case of differences between implied and mean returns defines the usage of relation (39) for the definition of matrices P and Q. The option (39) is also applied in this simulation work. The calculations have been performed with 7 × 7 identity matrix P, \n\n\n\n\n\n1\n\n\n…\n\n\n0\n\n\n\n\n⋯\n\n\n1\n\n\n…\n\n\n\n\n0\n\n\n…\n\n\n1\n\n\n\n\n\n 7 × 7 and two types of matrices Q:
9.3.5 Evaluation of the BL returns EBL and the BL covariance matrix ΣBL
\n
The evaluations of the modified mean assets’ returns EBL according to the BL model are done according to relations (43) and (44). The value of the covariance matrix of the expert views is assumed to be as the historical covariance ∑ but the values of its components are decreased with equal value \n\nτ\n\n. Thus the covariance matrix of the expert views is \n\nτ\n∑\n\n where the value of \n\nτ\n\n must be between 0 and 1. From practical recommendations [7, 16, 17], this research uses \n\nτ\n=\n0.5\n\n. The BL model evaluations are.
9.3.6 Solution of portfolio problem with \n\n\nE\nBL\nT\n\n\n and ΣBL
\n
The portfolio problem (11) is repetitively solved by changing \n\nΨ\n∈\n\n0\n1\n\n\n with the BL evaluations of the assets’ characteristics \n\n\nE\nBL\nT\n\n\n and ΣBL. The new BL “efficient frontier” is found as a set of numerically evaluated points (100 points). For illustration purposes both “efficient frontiers” with historical data (MV model) and BL data (BL model) are given in Figure 11.
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Figure 11.
Efficient frontiers with MV and BL models.
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\n
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9.3.7 Evaluation of the BL weights \n\n\nw\nBL\nopt\n\n\n\n
\n
The portfolio which has maximum Sharpe excess ratio is identified. This maximum is found from the numerically evaluated points of the BL “efficient frontier.” The needed portfolio parameters are stored in the arrays in MATLAB, during the sequential solutions of problem (11). The Sharpe excess ratio evaluated from (45) gives:
The difference between \n\n\nw\nBL\nopt\n\n\n and wopt shows a bit increase of the weight for the second asset (PROFIT) for the BL portfolio.
\n
\n
\n
\n
9.4 Comparison of the MV solution wopt and the BL one \n\n\nw\nBL\nopt\n\n\n\n
\n
The optimal weights \n\n\nw\nBL\nopt\n\n\n and wopt are assumed to be implemented as portfolio solutions in the beginning of month of September 2018. At the end of this month we can estimate the actual mean returns of the assets for month of September Ef and the modified actual covariation matrix \n\n\n∑\nf\n\n\n which is calculated again for 8 months history but from February to September 2018.
For the case when the MV weights wopt are invested the investor results will be
Then these portfolio results will be compared in the space Risk(Return). The portfolio point which is situated far on the Nord-West direction of the Risk(Return) space is the preferable portfolio. Such assessment will prove which portfolio model MV or BL gives more benefit and efficiency.
\n
\n
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9.5 Multiperiod portfolio optimization
\n
Following Figure 6 a next portfolio investment with MV and BL models is done by moving the history period 1 month ahead. The portfolio evaluations are done for a history period from February till September 2018. The evaluated weights \n\n\nw\nBL\nopt\n\n\n and wopt are applied for the month of October. For this case of 8 months historical period and available data for all 12 months of 2018 such multiperiod investment policy will evaluate 4 portfolios using the two models MV and BL. This research did three modifications of the BL model, concerning the evaluation of the matrices P and Q, related to the views for changing the assets characteristics:
For the cases when all components (\n\nП\n−\nE\n\n) or П have same sign, the procedures (32) or (33) are applied. The obtained results are given in Table 1.
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
MV model
\n
BL model
\n
\n
\n
P(\n\nα\n\n)
\n
P(\n\nП\n−\nE\n\n)
\n
P(\n\nП\n\n)
\n
\n\n\n
\n
Return (MV)f
\n
Risk (MV)f
\n
Return (BL)f
\n
Risk (BL)f
\n
Return (BL)f
\n
Risk (BL)f
\n
Return (BL)f
\n
Risk (BL)f
\n
\n
\n
0.1080
\n
0.0133
\n
0.1017
\n
0.0132
\n
0.1055
\n
0.0132
\n
0.1122
\n
0.0129
\n
\n
\n
−0.0187
\n
0.0117
\n
−0.0931
\n
0.0120
\n
−0.0632
\n
0.0111
\n
−0.0221
\n
0.0106
\n
\n
\n
−0.4011
\n
0.0282
\n
−0.3861
\n
0.0263
\n
−0.3793
\n
0.0255
\n
−0.4088
\n
0.0292
\n
\n
\n
−0.3525
\n
0.0240
\n
−0.2313
\n
0.0114
\n
−0.1523
\n
0.0080
\n
−0.2028
\n
0.0106
\n
\n
\n
Mean values
\n
\n
\n
−0.1661
\n
0.0193
\n
−0.1552
\n
0.0157
\n
−0.1223
\n
0.0145
\n
−0.1304
\n
0.0158
\n
\n\n
Table 1.
Results of multi-period portfolio management with MV and BL models.
\n
The graphical presentation of the comparison of the multiperiod portfolio management between MV and BL with P(\n\nП\n\n) modification is given in Figure 12.
\n
Figure 12.
Comparison of multiperiod MV and BL(P(П)) portfolio optimization.
\n
The common results prove that the market situation in 2018 does not allow the mutual funds to achieve positive return. The results are negative but this negative value is less than the riskless return value rf = −0.4. Hence, the portfolio management allows reduction of the losses. Particularly, all three modifications of the BL model give better results in comparison with the classical MV portfolio model. The mean values of the returns with BL model are very close to the returns of the MV model. But the risk values are considerably lower, which means that the probability to be closer to the mean values of BL returns is higher than the case of MV model.
\n
\n
\n
\n
10. Time management considerations for the portfolio investments
\n
This research illustrates that the task of portfolio investment is quite complicated. The meaning of portfolio optimization concerns the definition and solution of portfolio problem. In both these tasks the time is a prerequisite for successful portfolio investment.
\n
\n
10.1 Time requirements for the stage of definition of the portfolio problem
\n
The content in the paragraph “Portfolio optimization problem” explicitly asserts that the investor has to choose the duration of the historical period. This duration, n is in discrete form. It has to be chosen in a way that can refer to the investment period (T-t0). Obviously, high number of n will give influence for the slow changes in the market behavior. Respectively, the active portfolio management will not benefit with long duration of the historical period n.
\n
The active management needs to follow the current dynamics of the market. The relations between n and (T-t0) cannot be derived on theoretical basis. Only practical considerations could be useful. The authors’ experience recommends duration of the historical period to be considered between 6 and 8 months. Such history period can be used for multiperiod portfolio management from 1 to 3 months ahead in the future.
\n
An unexpected problem has been met by the authors, concerning the relation between the historical discrete points n and the number N of the assets, included in the portfolio. The two parameters n and N participate both for the evaluation of the covariance matrix ∑. This matrix should be in full rank by means that the portfolio problem (11) must generate regular solutions. If the rank of ∑ is less than N problem (11) gives unrealistic solutions. To keep ∑ with rank N it is needed its components to be evaluated with historical data n > N. The practical minimal case is n + 1 = N but before solving the portfolio problem the investor has to check the rank of ∑. As practical consideration, if the portfolio contains many assets and N is high, the data from the historical period n have to be also high. For that case one can use not only monthly returns but also weekly average data. Thus, the value of n can increase.
\n
\n
\n
10.2 Time requirements for the solution of the portfolio problem
\n
The solution of the portfolio problem (11) gives unique set of weights, which have to be implemented for the portfolio investment. Because the market behavior changes, reasonable policy is to perform repeatedly definition and solution of the portfolio problem. Potential beneficial strategy can be the multiperiod portfolio management, presented in Figure 6. It incorporates the multiperiod management and adopts the portfolio parameters with up to date market data. The relation between the duration of the historical period and the investment period is still an open question. But making additional simulations with 1, 2, 3 or more months (time) ahead the portfolio manager can change his decision on each investment step.
\n
\n
\n
\n
11. Conclusions
\n
This research identifies in explicit way the influence of the time for the definition and solution of portfolio problems. These time requirements are considerably related with the estimation of the parameters of the portfolio problem. Respectively, the time requirements insist the portfolio management to be performed in multiperiod investment.
\n
This research makes an analysis of the development of the portfolio theory. Starting with the Markowitz formalization, the MV portfolio problems are based only on historical data about mean returns and covariances between the returns. The development of CAPM gives new relations, originated from a new “market” point. The last gives additional information about the values of the parameters of the portfolio problem. Finally, the BL model introduces a new set of points, “implied excess returns,” which originate from the market point. As a result, new values for the parameters of the portfolio problem are found. Respectively, the portfolio problem gives weights of the assets, which are not sharp cut, which decreases the risk of the investment.
\n
This research introduces new modifications of the BL model for the part of definition of expert views. Particularly the experts are substituted by additional data, which origins from the dynamical behavior of the assets’ returns. Thus, not only mean returns and covariances are taken into consideration, but also the difference between objective parameters as implied and historical mean returns. These modifications allow the portfolio model MV and these based on BL one to be compared on a common basis and to assess their performances. Such comparison cannot be made if subjective experts are used, because their mutual views will be different for the same historical data and with changes the members of the experts.
\n
This research gives also a practical added value with the analysis of the behavior of the market with mutual funds in Bulgaria. This gives additional experience and bases for future comparisons and assessments of the different portfolio models.
\n
\n
Acknowledgments
\n
This work has been partly supported by project H12/8, 14.07.2017 of the Bulgarian National Science fund: Integrated bi-level optimization in information service for portfolio optimization, contract ДH12/10, 20.12.2017.
\n
\n',keywords:"data driven analysis, real-time portfolio optimization, decision making, automation in information systems",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/69072.pdf",chapterXML:"https://mts.intechopen.com/source/xml/69072.xml",downloadPdfUrl:"/chapter/pdf-download/69072",previewPdfUrl:"/chapter/pdf-preview/69072",totalDownloads:295,totalViews:0,totalCrossrefCites:0,dateSubmitted:"June 7th 2019",dateReviewed:"August 2nd 2019",datePrePublished:"September 14th 2019",datePublished:"March 4th 2020",dateFinished:null,readingETA:"0",abstract:"The time management is important part for tasks in real-time operation of systems, automation systems, optimization in complex system, taking explicit consideration in time constraints, scheduling of tasks and operations, making with incomplete data, and time management in different practical cases. The limit in time for taking appropriate decisions for management and control is a strong constraint for the implementation of autonomic functionalities as self-configuration, self-optimization, self-healing, self-protection in computer systems, transportation systems, and distributed systems. Time is an important and expensive resource. The time management in financial domain is a prerequisite for high competitiveness and an increase in the quality of the investment activities. It is the popular phrase that time is money, and particularly, the portfolio optimization targets its implementation in real cases. This research targets the identification of portfolio parameters, which are strongly influenced by time. We restrict our considerations only on portfolio optimization task, and we identify cases, which are strongly influenced by time constraints. Thus, the portfolio optimization problem is discussed on position how the time can influence the portfolio characteristics and solutions. This chapter starts with the description of the object portfolio management, which provides the cases where time in explicit way influences the portfolio problem.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/69072",risUrl:"/chapter/ris/69072",signatures:"Todor Atanasov Stoilov, Krasimira Petrova Stoilova and Miroslav Dimitrov Vladimirov",book:{id:"9332",title:"Application of Decision Science in Business and Management",subtitle:null,fullTitle:"Application of Decision Science in Business and Management",slug:"application-of-decision-science-in-business-and-management",publishedDate:"March 4th 2020",bookSignature:"Fausto Pedro García Márquez",coverURL:"https://cdn.intechopen.com/books/images_new/9332.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"22844",title:"Prof.",name:"Fausto Pedro",middleName:null,surname:"García Márquez",slug:"fausto-pedro-garcia-marquez",fullName:"Fausto Pedro García Márquez"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"47367",title:"Prof.",name:"Krasimira",middleName:"petrova",surname:"Stoilova",fullName:"Krasimira Stoilova",slug:"krasimira-stoilova",email:"k.stoilova@hsi.iccs.bas.bg",position:null,institution:null},{id:"51706",title:"Prof.",name:"Todor",middleName:null,surname:"Stoilov",fullName:"Todor Stoilov",slug:"todor-stoilov",email:"todor@hsi.iccs.bas.bg",position:null,institution:{name:"Bulgarian Academy of Sciences",institutionURL:null,country:{name:"Bulgaria"}}},{id:"307620",title:"Dr.",name:"Miroslav",middleName:null,surname:"Vladimirov",fullName:"Miroslav Vladimirov",slug:"miroslav-vladimirov",email:"vladimirov@ue-varna.bg",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Portfolio optimization problem",level:"1"},{id:"sec_3",title:"3. Modern Portfolio Theory",level:"1"},{id:"sec_4",title:"4. Capital Market Theory",level:"1"},{id:"sec_5",title:"5. Black-Litterman model for estimation of portfolio characteristics",level:"1"},{id:"sec_6",title:"6. Definition of the “implied excess returns”",level:"1"},{id:"sec_7",title:"7. Definition of P and Q from scientific views",level:"1"},{id:"sec_8",title:"8. BL modification of the assets’ characteristics",level:"1"},{id:"sec_9",title:"9. Numerical simulations and comparisons between MV and BL portfolios solutions",level:"1"},{id:"sec_9_2",title:"9.1 Initial evaluation of historical data",level:"2"},{id:"sec_10_2",title:"9.2 Evaluation of the efficient frontier with MV model for the first 8 months",level:"2"},{id:"sec_11_2",title:"9.3 Evaluation of the assets’ characteristics for the BL model",level:"2"},{id:"sec_11_3",title:"9.3.1 Definition of the risk-free return rf",level:"3"},{id:"sec_12_3",title:"9.3.2 Evaluation of the market point",level:"3"},{id:"sec_13_3",title:"9.3.3 Evaluation of the implied excess returns Пi, i = 1,…,N.",level:"3"},{id:"sec_14_3",title:"9.3.4 Definition of the characteristics of the expert views P and Q",level:"3"},{id:"sec_15_3",title:"9.3.5 Evaluation of the BL returns EBL and the BL covariance matrix ΣBL",level:"3"},{id:"sec_16_3",title:"9.3.6 Solution of portfolio problem with \n\n\nE\nBL\nT\n\n\n and ΣBL",level:"3"},{id:"sec_17_3",title:"9.3.7 Evaluation of the BL weights \n\n\nw\nBL\nopt\n\n\n\n",level:"3"},{id:"sec_19_2",title:"9.4 Comparison of the MV solution wopt and the BL one \n\n\nw\nBL\nopt\n\n\n\n",level:"2"},{id:"sec_20_2",title:"9.5 Multiperiod portfolio optimization",level:"2"},{id:"sec_22",title:"10. Time management considerations for the portfolio investments",level:"1"},{id:"sec_22_2",title:"10.1 Time requirements for the stage of definition of the portfolio problem",level:"2"},{id:"sec_23_2",title:"10.2 Time requirements for the solution of the portfolio problem",level:"2"},{id:"sec_25",title:"11. Conclusions",level:"1"},{id:"sec_26",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Markowitz H. Portfolio selection. Journal of Finance. 1952;7:77-91\n'},{id:"B2",body:'Sharpe W. Portfolio Theory and Capital Markets. New York: McGraw Hill; 1999, 316 p. Available from: https://www.amazon.com/Portfolio-Theory-Capital-Markets-William/dp/0071353208\n\n'},{id:"B3",body:'Merton C. An analytic derivation of the efficient portfolio frontier. Journal of Financial and Quantitative Analysis. 1972;7(4):1851-1872. DOI: 10.2307/2329621. Available from: https://www.jstor.org/stable/2329621?seq=1#page_scan_tab_contents. http://www.stat.ucla.edu/∼nchristo/statistics_c183_c283/analytic_derivation_frontier.pdf\n\n'},{id:"B4",body:'Kolm N, Ritter G. On the Bayesian interpretation of Black-Litterman. European Journal of Operational Research. 2017;258(2):564-572. Available from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2853158\n\n'},{id:"B5",body:'Palczewski A, Palczewski J. Black-Litterman model for continuous distributions. European Journal of Operational Research. 2018;273(2):708-720. DOI: 10.1016/j.ejor.2018.08.013, Available from: https://ideas.repec.org/a/eee/ejores/v273y2019i2p708-720.html\n\n'},{id:"B6",body:'Pang T, Karan C. A closed-form solution of the black-Litterman model with conditional value at risk. Operations Research Letters. 2018;46(1):103-108. DOI: 10.1016/j.orl.2017.11.014. Available from: https://www.sciencedirect.com/science/article/pii/S0167637717306582?via%3Dihub\n\n'},{id:"B7",body:'He G, Litterman R. The Intuition behind Black-Litterman Model Portfolios. New York: Investment Management Research, Goldman Sachs & Company; 1999. Available from: https://faculty.fuqua.duke.edu/∼charvey/Teaching/IntesaBci_2001/GS_The_intuition_behind.pdf. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=334304\n\n'},{id:"B8",body:'Walters J. The Black-Litterman Model in Detail. 2014. Available from: https://systematicinvestor.wordpress.com/2011/11/16/black-litterman-model/\n'},{id:"B9",body:'Walters J. Reconstructing the Black-Litterman Model. 2014. Available from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2330678\n\n'},{id:"B10",body:'Satchell S, Scowcroft A. A demystification of the black–Litterman model: Managing quantitative and traditional portfolio construction. Journal of Asset Management. 2000;1(2):138-150. DOI: 10.1057/palgrave.jam.2240011. Available from: https://link.springer.com/chapter/10.1007%2F978-3-319-30794-7_3. https://www.researchgate.net/publication/31962785_A_demystification_of_the_Black-Litterman_model_Managing_quantitative_and_traditional_portfolio_construction\n\n'},{id:"B11",body:'Vladimirov M, Stoilov T, Stoilova K. New formal description of expert views of Black-Litterman asset allocation model. Journal Cybernetics and Information Technologies. 2017;17(4):87-98. DOI: 10.1515/cait-2017-0043, Available from: http://www.cit.iit.bas.bg/CIT_2017/v-17-4/05_paper.pdf\n\n'},{id:"B12",body:'URL1. Available from: http://infostock.bg\n\n'},{id:"B13",body:'URL2. Available from: www.baud.bg\n'},{id:"B14",body:'URL3. Available from: www.fsc.bg\n'},{id:"B15",body:'URL4. Available from: https://www.bnb.bg/Statistics/StBIRAndIndices/StBILeoniaPlus/index.htm\n\n'},{id:"B16",body:'Allaj E. The Black-Litterman model: A consistent estimation of the parameter tau. Financial Markets and Portfolio Management. 2013;27(2): 217-251 DOI: 10.1007/s11408-013-0205-x. Available from: https://www.researchgate.net/publication/257417995_The_Black-Litterman_model_A_consistent_estimation_of_the_parameter_tau\n\n'},{id:"B17",body:'Allaj E. The Black-Litterman model and views from a reverse optimization procedure: An out-of-sample performance evaluation. Electronic Journal. July 18 2017:1-32. DOI: 10.2139/ssrn.2999335. Available from: papers.ssrn.com/sol3/Papers.cfm?abstract_id=2999335\n\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Todor Atanasov Stoilov",address:"todor@hsi.iccs.bas.bg",affiliation:'
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UK Research and Innovation (former Research Councils UK (RCUK) - including AHRC, BBSRC, ESRC, EPSRC, MRC, NERC, STFC.) Processing charges for books/book chapters can be covered through RCUK block grants which are allocated to most universities in the UK, which then handle the OA publication funding requests. It is at the discretion of the university whether it will approve the request.)
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