Combined Water-Oxygen Pinch Analysis with Mathematical Programming for Wastewater Treatment

第6卷第6期过程工程学报Vol.6 No.62006年12月The Chinese Journal of Process EngineeringDec. 2006Combined Water -Oxygen Pinch Analysis with MathematicalProgramming for Wastewater TreatmentSONG Li-l(宋丽丽)，DU Jian(都健)，CHAI Shao-bin(柴绍斌)，YAO Ping-jing(姚平经)(School of Chemical Engineering, Dalian University of Technology, Dalian, Liaoning 116012, China)Abstract: Water - oxygen pinch analysis is an effective method to decrease the wastewater quantity and improve thewastewater quality. But when multiple-contaminants are present, the method is difcult to be carried out. In this paper, themethod that combines water- oxygen pinch analysis with mathematical programming is proposed. It obtains the generaloptimal solution and leads to the reuse stream that cannot be found only by pinch analysis. The new method is ilustrated byan example, and the annual cost is reduced by 8.43% compared with the solution of literature.Key words: water-oxygen pinch analysis; wastewater minimization; mathematical programmingCLC No.: TQ021Document Code: AArticle ID: 1009- 606X(2006)06- -0932- -05INTRODUCTIONwater allocation in a petroleum refinery based on asuperstructure of all possible reuse and regenerationIn recent years, there has been considerableopportunities. Doyle et al.", Alva-Argaez et al.8l asdevelopment of system engineering methods to achievewell as Huang et al.91 also presented MINLP and NLPfresh water and wastewater minimization in industry.models in series. Savelski and Bagajewicz presented theThis is driven by the rising cost of fresh water andnecessary conditions of optimality of water utilizationeffuent treatment, as well1S morestringentsystems in process plants with single contaminant andenvironmental legislation. At present, there are twomultiple contaminants respectively to reduce a nonlinearmainapproaches used to design water utilizationprogram to a linear program, by inserting the maximumnetwork, that is, conceptual approach and mathematicaloutlet concentration conditionslol. In recent years,programming.mathematical programming has been developed greatly1.1 Conceptual Design Approachby combining with advanced algorithms and optimizingIn 1994, Wang et al."] introduced the importantapproaches, such as, genetic algorithms, simulatedconcepts of“water pinch"" and“limiting water profile”annealing algorithm, particle swarm optimizations andand proposed a targeting procedure that allows theneural network approach.calculation of the minimum fresh water usage withoutIn all of above reports, it is rarely mentioned tothe need of constructing a network. Although thiscombine water pinch with mathematical programming.approach is a major step in understanding water systemAt present, there is no any paper on combineddesign, it has several limitations. Dhole et al.2 correctlywater- oxygen pinch analysis with mathematicalpointed out that based on a mass transfer model was aprogramming. This paper presents a new approach tolarge drawback and presented an alternative method. Insolve the problems.2000, Polley et al.5) presented a similar representationwith Dhole's and thus overcame the limitations based on2 COMBINED WATER-OXYGENthe mass transfer-based approach. Halle! presented aPINCH ANALYSIS METHODOLOGYnew graphical targeting method which introduced a newrepresentation of water composite curves by“waterThe aim of this methodology is to enhance the costpurity”and the concept of“water surplus". Besideseffectiveness of wastewater treatment and decrease thewater pinch, Zhelev et al.5 presented oxygen pinchpollution levels in wastewater treatment process. Thewhich was prior to designing the minimum oxygenfactors contributing to the cost of wastewater treatmentconsumption required by micro-organisms for wasteand pollution levels are the wastewater quantity and thedegradation.wastewater quality. Water pinch analysis is focused on1.2 Mathematical Programmingthe中国煤化工wastewater, but can'tTakama et al.6 addressed an approach for optimalimpr.MYHCNMHGOxygen pinch analysisReceived date: 2005- -08- -30; Acepted date: 2006 -01-13Blograpby:第6期SONG Li-li, et al: Combined Water- Oxygen Pinch Analysis with Mathematical Programming for Wastewater Treatment 933was found effective to solve the problem'9.shown as Fig.l(a). Since the relation is usually not2.1 Oxygen Pinch Analysislinear, it is difficult to use it in pinch analysis. However,Since almost all wastewater can be treatedthe reciprocal of substrate concentration and thebiologically withproper environmental control,reciprocal of D follow a linear correlation. Oxygenbiological treatment has been widely used as core partpinch analysis is defined by graphical targeting methodof the treatment processes. In biological treatment,similar to water pinch analysis [shown in Fig.1(b) andwaste substances are oxidized and converted into simple1(c)].end products， in which the oxidizer is oxygenThe oxygen pinch concept focuses on mass transfertransferred from air into the liquid. Oxygen demand ispinch analysis but exceeds the classical pinch targetdirectly related to not only wastewater quality but alsoexpectations. It succeeds to set quantitative targetsenergy required. So oxygen pinch analysis was(oxygen solubility, residence time, oxidation energynecessary to design the minimum oxygen consumptionload), as well as additional qualitative targets, namelyrequired by the micro-organisms for waste degradationthe growth rate directly addressing the micro-organismsand suggest flowsheet.age and health. Water pinch and oxygen pinch areOxygen demand D is proportional to substrateshown in Fig.2.concentration S, the relationship between D and S isr1单二>S古(旧) Relationship(6) Linear trace(C) Oxygen pinchFig.1 Oxygen pinch stream definitiss'lPinchMinimum freshMinimum oxygenwaterconsumiptionm. Fig.2 Water pinch and oxygen pinch analyses2.2 Water- Oxygen Pinch Analysistreatment was achieved by the application of aThe factors contributing to the cost of wastewatercombined water- oxygen pinch analysis (shown intreatment and pollution levels are the wastewaterFig.3). Moreover, the proposed combination methodquantity and the wastewater quality. The wastewaterwill allow to realize better management of fresh waterquantity is directly related to the amount of energyand wastewater.required for the wastewater treatment, as well aspollution levels. W ater pinch analysis was proposed toWater uilizationdecrease the wastewater quantity thereby decreasing thesystems<-- Water pinch analysiscost of wastewater treatment and pollution levels. Thewastewater quality was inversely propotional to the中国煤化工Water pinch analysisenergy required for wastewater treatment as well asOxygen pinch analysisCNMHGpollution levels. Oxygen pinch analysis was presentedo improve the wastewater quality. Thus the overallDisposaleffect of increasing the cost effectiveness of wastewaterFig.3 Water system with water- oxygen pinch analysis934过程工程学报第6卷The link between these two pinch analyses is theusage of COD，chemical oxygen demand, as theconcentration variable in water pinchanalysis.-CTP1Water- oxygen pinch analysis can be simple as waterpinch analysis with COD as concentration variable.[2]9-》心-3 COMBINED WATER- -OXYGENPINCH ANALYSIS WITH-[TP3MATHEMATICALPROGRAMMING FORFig.4 Superstructure model of wastewater treatment networksWASTEWATER TREATMENTwater- oxygen pinch complies with the water pinchThe conceptual design approach leads to thedesignrules.Streams whose contaminationminimum fresh water requirement of the entire processconcentration is higher than that of the pinch are fullyin a direct way, but when multiple-contaminants aretreated by the treatment process, those that are equal topresent, graphicalmethodsrequireadditionalthe pinch are partially treated and partially bypass theassumptions to ease the implementation, some of whichtreatment, and those that are lower than the pinchmay be difficult to justify. The mathematicalcompletely bypass the treatment. According to theprogramming methods are effective in optimizing large-design rule, the streams partially treated are regarded asscale systems, but are difficult to interpret, givingparameters, while streams fully treated and completelydesigners fewer insights compared with graphicalbypass the treatment are regarded as constants. So themethods, and when the system is too large, it is alsoamount of uncertain parameters is deceased largely.difficult to obtain the general optimal solution. These3.3 Setting up Mathematic Modelcan be solved by combined pinch analysis withThe capital cost and operating cost functions ofmathematical programming for wastewater treatment.treatment process are expressed by wastewater flowrate,3.1 Setting up the Model of Wastewater Treatmentand the mathematical model is shown as follows:NetworkObjective function:The wastewater treatment network is described as asystem, in which wastewater can be treated more thanMin2.(ASP +yB,J).(1)once, including multiple streams and multiplewastewater treatment processes. The flowrate to eachSubject to:wastewater treatment process have been given. The(1) Mass balance of wastewater treatment process t:removal ratio of each treatment process is constant.Ex.=..x.+m.(2)Entering wastewater treatment network, eachstream flows into a splitting node, where the stream can(2) Contaminant mass balance of wastewater treatmentflow to all wastewater treatment processes. There is aprocess t:mixing node in font of each treatment process, whereall streams coming from other operation units are mixed.There is another splitting node behind each treatmentprocess, in which stream may flow to discharge node or(3) Mass balance of wastewater stream w:mixing nodes. And all wastewater streams flow to amixing node at last, namely the discharge node, where2x. +x.=1.(4)the concentration of contaminant must satisfy theenvironmental regulations. In Fig.4, the superstructure(4) Flowrate limiting of wastewater treatment process t:model of wastewater treatment network includes threewastewater streams, three wastewater treatmentEx..≤4(5)processes and a discharge pool.中国煤化工，istewater in discharge3.2 Decreasing Uncertain Parameter byWater-Oxygen Pinch Analysis:YHCNMHGThe water- oxygen pinch can be solved from theprocedure presented by Zhelev et al.!59. Furthermore, theEixcusm + xExC.m<(E.J.)es. (6) .第6期SONG Li-li, et al.: Combined Water- _Oxygen Pinch Analysis with Mathematical Programming for Wastewater Treatment 935It is ofen difficult to obtain the general optimumand the environmental limiting concentrations of thesolution for non-linear programming by GAMSthree contaminants are 5, 20, 100 mg/L, respectively.(General Algebraic Modeling System). Applying thConsidering the minimum oxygen consumptionrule of water- oxygen pinch analysis to decrease therequired by the micro-organisms for waste degradation,number of uncertain parameters, the superstructure isthe concentrations are turned into the COD as shown ineasy to solve for the general optimum solution.Table 3, in which suspended solid can't be regeneratedby biological treatment and is not necessary to turn into4 CASE STUDYCOD.The case is taken from Kuo et al.'2]. ThreeTable 1 Wastewater stream data for the case studywastewater streams are produced and must be treatedStream number Flowrate (th).Contaminant concentration (mgL)__before discharge. The flowrates of streams and theH2SSuspended solidconcentrations of contaminants involved are given in13.1390125032.716780 11400Table 1. The parameters of treatment processes,56.5251035removal rates and the cost functions are given in Table 2,Table2 Removal rate and cost function for treatment processRermoval rate (%)CostTreatment process0i1Suspended solid Capital cost (S)Operaing cost (S/b)_TP999016 800f01.0fTPII907012 600/0.70.0067%TPm504800/97Annual rate ofreturn (%) 2=10Operating time (h/a)y-8600 .Table 3 COD concentration of wastewater streamContaminant concentation (mg/L)Stream noumberFlowrate (th)COD (H2S)COD (Oi)Total COD732.6732.57766.6931523.51.358.2931944.17_56.546.94 .325.71372.77According to the given parameters and data, th5 DISCUSSIONsuperstructure and mathematical model are set up. Then,Compared with the result by Kuo et al.12), thethe water- -oxygen pinch ftom the procedure presentedby Zhelev et al.5] is solved. The pinch of COD (H2S) isannual cost ●of the optimal wastewater treatmentat 732.67 mg/L, so stream 1 is considered as parareternetwork in this paper is lowered by 8.43%. It can beand stream 2, 3 are considered as constants in thelearned that the two networks are mainly different in thewastewater treatment. According to the procedure, otherflowrate of stream 1 to TP1 and the reused stream ofcontaminants are similarly confirmed. The number o1TP2. Conceptual design approach adopted by Kuo etuncertain parameters is decreased greatly by water-al."l2] failed to achieve the general optimal solutionoxygen pinch analysis and the superstructure is solvedbecause they simplified the design procedure by ruleseasily. We obtain the following optimal wastewaterand assumptions. Moreover, they did not consider thetreatment network as shown in Fig.5. The optimalcost difference between the treatment processes. It isannual cost is $352095.3772, lowed by 8.43%, asevidently that the operating cost of TP1 is much morecompared with the result by Kuo et al."4, which wasthan one of TP2 and the annual total cost can be reducedby decreasing the flowrate to TPI. Water- oxygen pinch$384 489.7694.analysis combined with mathematical programming can3274@27次M2.7%[TP ]227盟回set up all possibilities of the network and get the optimalresult.13.1收11 MS56792[ Tm2中国煤化工48.956业43.499 t6.5038-44544[ TP3 ].544的YHC N M H Gat combines water-oxygen pinch analysis with mathematical programmingFig,5 The optimal wastewater treatment network in this workis introduced to solve wastewater treatment network.936_过程工程学报第6卷Firstly, water- -oxygen pinch analysis is an effectiveREFERENCES:method to decrease the quantity and improve the quality[1] Wang Y P, Smith R. Wastewater Minimization []. Chem. Eng. Sci,of wastewater. Then, the amount of uncertain parameter1994, 49(7): 981-1006.[2] Dhole V R, Ramchandani N, Tainsh R A, et al. Make Your Processof superstructure and mathematical model is reducedWater Pay for Ief[J]. Chem. Eng, 1996, 103(1): 100-103.greatly by pinch analysis. Finally, the method of[3] Polley G T, Polley H L. Design Better Water Networks [0]. Chem.water- - oxygen pinch analysis combined mathematicalEng. Prog, 2000, 96(2): 47-52.programming can obtain the global optimal solution and[4] Hallal N. A New Graphical Targeting Method for Waterfind the stream that cannot be found by pinch analysis.Minimistion [切. Adv. Environ. Res, 2002, (6): 377-390.The new method is illustrated by a case, and the annual[5] Zhelev T K, Bhaw N. Combined Water- Oxygen Pinch Analysis forcost is reduced by 8.43% compared with the solution byBetter Wastewater Treatment Management []. Waste Managc, 2000,Kuo et al.!42.20(8): 665 670.[6] Takama N, Kuriyama T, Shiroko K, et al. Optimal Water AllocationNOTATIONS: .in a Petroleum Refinery []. Comput. Chem. Eng， 1980, 4(4):An Capital cost coficnt of tratmenet procss t($/t)251-258.Operation cost cofcient of treatment process t [$/(t:b)][7] Doyle s J, Smith R. Targeting Water Reuse with MultipleThe enviromental discharge limiting concentration of contaminant jContaminants [0] Trans. IChemE, Part B, 1997, 75(3): 181-189.(mg/L)[8] Alva-Argiz A, Vallianatos A, Kokossis C. A MulticontaminantTransshipment Model for Mass Exchange Networks and WastewaterMinimisation Problems [0 Comput Chem. Eng, 1999, 23(10):Flowrate of wastewater stream w (/h)1439-1453.Limiting flowrate of water treatment process (h)[9] Huang C H, Chang C T, Ling H C, et al. A MathematicalRemoval rate of contamninant j in treatnent processtProgramming Model for Water Usage and Treatment NetworkwReuse flowrate of wastewater (h)Design [0]. Ind. Eng. Chem. Res, 199, 38(7): 2666 2679.Discharge flowrate from treatment process to environment (/)Discharge flowrate fom wastewater stream to environment (Uh)[10] Savelski M J, Bagnjewicz M J. On the Optimality Conditions ofFlowrate from treatment process k to treatment process t (Uh)Water Utilization Systems in Process Plants with SingleFlowrate of wastewateam w to treatmen proces t(th)Contaminants []. Chem. Eng. Sci, 2000, 522): 5035 -5048.[1] Savelski M J, Bagjewicz M J. On the Nccessary Conditions ofExponential coefficient of capital cost of treatmeat process tOptimality of Water Uilization Systerms in Process Plants withAnnual rate of capital cost return (%)SubscribeMultiple Contaminants [D]. Chem. Eng. Sci, 2003, 58(24):Reuse processEnvironment5349 -5362. .Treatment processContaminant[12] Kuo W C J, Smith R Efluent Treatment System Design凹. Chem.Wastewater streamutOutletEng. Sci, 1997, 52(23): 4273- 4290.中国煤化工MYHCNMHG