第21卷第1期計算機與應(yīng)用化學(xué)Vol 21, No. I004年1月28日Computers and Applied ChemistryJanuary 2004換熱網(wǎng)絡(luò)的分析楊瑩,高維平吉林化工學(xué)院化學(xué)工程系,吉林,132022)摘要:通過對換熱網(wǎng)絡(luò)的研究發(fā)現(xiàn),當物流有分流時,換熱網(wǎng)絡(luò)分析的數(shù)學(xué)模型為非線性規(guī)劃問題。本文給出換熱網(wǎng)絡(luò)分析的非線性規(guī)劃模型,同時優(yōu)化各路分流的流量及換熱單元進岀口溫度。經(jīng)模型轉(zhuǎn)化,用復(fù)合形法與線性規(guī)劃法的雙層組合求解,成功地解決了換熱網(wǎng)絡(luò)分析中非線性規(guī)劃的求解問題。經(jīng)實例考核計算證明,本文所建立的數(shù)學(xué)模型是正確可靠的,使用的雙層組合法與其它方法相比,方法簡單實用,結(jié)果準確,可在工程研究、設(shè)計中應(yīng)用,分析后所得的最佳參數(shù)可大大提高換熱網(wǎng)絡(luò)的熱回收量,節(jié)能效益十分顯著。關(guān)鍵詞:換熱網(wǎng)絡(luò):分析;非線性規(guī)劃中圖分類號:TQ015.9文獻標識碼文章編號:10014160(2004)01-135-140Analysis of heat exchanger networkYANG Ying and gAo WeiPingDepartment of Chemical Engineering Jilin Institute of Chemical Technology Jilin 132022, Jilin ChinaAbstract: When the streams are split the mathematical model in the analysis of heat exchanger network is non linear programming. Inthis paper the mathematical model of non-linear programming for optimal analysis of heat exchanger network is set up. Through conversion of the model the double layer combination of complex method and linear programming method is used to solve successfully te nonlinear programming problem of the heat exchanger network analysis. The practical examples showed that the mathematical modelexact. Compared with other methods the double layer combination method is simple and practical and can be applied to the improve-ment of heat exchanger networks with remarkable economic benefitKey words: heat exchanger network analysis, non-linear programmingYang Y and Gao WP. Analysis of heat exchanger network. Computors and Applied Chemistry 2004, 21(1): 135-140換熱網(wǎng)絡(luò)是能量回收利用中的一個重要子系線性規(guī)劃問題到目前為止還沒有通用、有效的求解統(tǒng)?，F(xiàn)有化工生產(chǎn)中的一些老裝置由于初建時技方法只能針對具體問題尋找求解方法。對于一個術(shù)比較落后對節(jié)能要求不高過程物流旳換熱不合復(fù)雜的換熱網(wǎng)絡(luò)流程其非線性規(guī)劃中的變量有時理有些生產(chǎn)工藝由于生產(chǎn)能力或條件的變化對已多達幾百個因此用現(xiàn)有的非線性規(guī)劃求解方法很有換熱網(wǎng)絡(luò)產(chǎn)生影響因此迫切需要調(diào)整改進。對難求解。W. Morton提出一種用于求解以投資費用現(xiàn)有網(wǎng)絡(luò)進行優(yōu)化分析是提高能量利用的有效方和能耗費用最小為目標函數(shù)的非線性規(guī)化問題的法它包括兩個主要問題第一要使各個換熱器的 FilterSQP方法1但這種方法僅限于優(yōu)化公用工程熱負荷及物流的進岀口溫度分配最優(yōu)第二對網(wǎng)絡(luò)費用本文提岀換熱網(wǎng)絡(luò)分析的非線性規(guī)劃模型并進行核算并對換熱面積作合理的調(diào)整。用復(fù)合形法與線性規(guī)劃法相結(jié)合的方法對此模型進關(guān)于換熱網(wǎng)絡(luò)的合成許多研究者已做了大量行求解可以同時求解各股分流的流量及各換熱器工作開發(fā)了不同的方法-11但對已有換熱網(wǎng)絡(luò)的換后溫度分析后所得的最佳參數(shù)可提高換熱網(wǎng)的分析與優(yōu)化則很少見諸文獻12-63。換熱網(wǎng)絡(luò)的絡(luò)的熱回收量分析即是對已合成出的或現(xiàn)有的換熱網(wǎng)絡(luò)進行整個系統(tǒng)的數(shù)學(xué)模擬預(yù)測在不同條件下系統(tǒng)的特性和1目標函數(shù)及約束條件行為借以發(fā)現(xiàn)其薄弱環(huán)節(jié)并加以改進。換熱網(wǎng)絡(luò)中國煤化工以最大熱回收量為目分析的數(shù)學(xué)模型可分線性規(guī)劃和非線性規(guī)劃對于標函又CNMH立以以阢化模型線性規(guī)劃已有多種有效的方法進行求解但對于非目標函數(shù):收稿日期:20030801;修回日期:2003-12-作者簡介:楊瑩(1972-),女,吉林人,碩士,講師計算機與應(yīng)用化學(xué)200421(=Wm(Tm-mn)→max(1)Wmm2為常數(shù)則目標函數(shù)和各約束式都是以冷、熱物流進、出口溫度為變量的線性函數(shù),可以應(yīng)滿足以下約束用線性規(guī)劃方法求解。冷熱物流交換熱量相等約束如果物流有分流且各路流量未知各股分流進Wei Thi- Thoi )-Wepi (toi -L)=0入相應(yīng)換熱單元的物流流量可以變化其熱容流率(2)也是變化的即有些W12不為常數(shù)是需優(yōu)化如果考慮熱損失可以把熱流的熱容流率W的變量時在以上數(shù)學(xué)模型中應(yīng)加入對分流點各路乘以一個熱利用率α,,α,一般取0.95~1.0分流流量的約束溫差約束Th-tom≥△tmThWfh(10)物流出口溫度約束Wl=12hwy≥7j=12ts≤t4kk=12灬…mcs(4)目標函數(shù)和約束式變?yōu)橐岳?、熱物流進、出口溫交換熱量大于或等于零約束:度和某些分流熱容流率為變量的非線性函數(shù)因此vm(Th-Thm)≥0該優(yōu)化問題就變?yōu)橐粋€非線性規(guī)劃問題。對于線性(5)規(guī)劃問題可以應(yīng)用原始單純形法、對偶單純形法及混合單元溫度約束:熱流混合單元要滿足式原始單純形二段法來求解對于非線性規(guī)劃問題采(6)用雙層求解法即在外層用復(fù)合形法優(yōu)化各分流的Talr-Thok, (1-Cphn/: )-2流量在內(nèi)層用線性規(guī)劃法優(yōu)化各換熱單元的最佳進出口溫度。(6)冷流混合單元要滿足式(7)2換熱網(wǎng)絡(luò)分析2.1線性規(guī)劃模型的轉(zhuǎn)化為了用線性規(guī)劃法求解,須將式(1)式(7)轉(zhuǎn)化為線性規(guī)劃數(shù)學(xué)模型。1)決策變量的確定如果換熱器的進口物流來自換熱網(wǎng)絡(luò)裝置之外則其進囗溫度確定否則將進口溫度選定為決策變量各換熱器冷、熱流的出口圖1物流混合示意圖溫度都是決策變量決策變量用U,表示。gram of stream(2)目標函數(shù)式(1)的轉(zhuǎn)化,將式(1)轉(zhuǎn)化成以下的形式leln-thok, (1 -Cpen/CpclJo=∑C(7)(3)熱平衡約束式(2)的轉(zhuǎn)化:為了將式(2)式6)中變?yōu)椤芶,1=b的形式,式2)左邊展開將常數(shù)項相加后移至右邊,即形成上式的形式。式(7)中,中國煤化工的轉(zhuǎn)化:將式3)轉(zhuǎn)CNMHG(9)化成∑,1≤b(1=n+1…,3n)的形式,b可以如果沒有物流分流或物流有分流時假設(shè)各分是正值,也可以是負值或零。在用線性規(guī)劃方法時,流的流量為已知且固定不變時各個換熱單元的冷、根據(jù)b的正負值決定引入松馳變量(b,≥0)或剩余熱物流流量一定忽略熱容流率隨溫度的變化,即變量或人為變量(b,<0)200421(1)楊瑩等換熱網(wǎng)絡(luò)的分析(5)對出囗溫度約束式4)的轉(zhuǎn)化:首先求出編號。通過上面的重新排序A的第m+mne+對熱冷流出口溫度有約束的決策變量數(shù)πhs和m列成為1個ne×neq的單位矩陣,此矩陣可作然后將式(4)轉(zhuǎn)化成以下形式為線性規(guī)劃的初始基礎(chǔ)矩陣B。在排序A時,同時點,≤b對應(yīng)地將b重新排序,這樣b就是初始基礎(chǔ)解(b為約束中常數(shù)項列矩陣)目標函數(shù)中松弛變量、i=3n+1…3n+mhs+mcs(12)剩余變量的系數(shù)C=0,人工變量的系數(shù)C=-M(6)交換熱量大于或等于零約束式(5)的轉(zhuǎn)M是一個充分大的正數(shù)化:式5)可以改寫成下面的形式:2.2復(fù)合形法模型的轉(zhuǎn)化Thi- Theh0≥0(13)為了用復(fù)合形法求解各分流流量將分流點約將式(13)轉(zhuǎn)化成束式(10)轉(zhuǎn)化為SW("mm)i= 3n +mhs + mcs +1r.. An +mhs +mcs(7)混合單元溫度約束式(6)的轉(zhuǎn)化:將式0≤Wo1≤W1i=12…h(huán)h=12,m(18)(6)轉(zhuǎn)化成下面的形式2.3各分流流量初值的確定i= 4n+ mhs + mcs +1, 4n mhs mcs+ na 15)分流點示意簡圖如下8)松弛變量、剩余變量、人工變量的引入數(shù)目以上轉(zhuǎn)化形成的約束條件中,對等式約束引入人工變量對不等式約束且b,≥0時,引入松弛變量;對于不等式約束且b,<0,引入剩余變量,并使b∈=-b,將不等式約束轉(zhuǎn)化成等式約束,即轉(zhuǎn)化成圖2熱流分流示意圖bi=12…neq(16)Fig. 2 Diagram of hot stream splitternn為決策變量n、松弛變量ne、剩余變量me和人工變量mmn的總和,即(1)在01謳區(qū)間上均勻產(chǎn)生隨機數(shù)a,,i=1nn nu t ne mne mnn并將約束方程重新排序,使之具有下列結(jié)構(gòu)形(2)將∑a規(guī)一化即a=a;/∑a式(3)各分流流量W;=W冷流分流流量初值確定方法與熱流相同。有幾個分流點以上步驟就重復(fù)幾次,這樣得到各路流量的初值。2.4迭代方法00分流流量確定后數(shù)學(xué)模型變?yōu)榫€性規(guī)劃問題進入內(nèi)層迭代求出各換熱單元的進出口溫度。各單元進出口溫度確定后再到外層用復(fù)合形法調(diào)整各欄在由處尸問反復(fù)迭代最后可以找A的第1~m行為引入松弛變量的那些行,松到滿中國煤化優(yōu)值弛變量從m+mne+l~m+mne+ne按行順序編CNMH求得最佳分流流量和換號。A的第ne+l~ne+me行為引入剩余變量的熱單元的最佳進出口溫度之后,須再判斷各股物流那些行,剩余變量從+1~mu+me按行順序編換熱是否達到了工藝要求。如果不滿足要選擇能號。A的ne+mne+l~neq行為引入人工變量的那量體加熱或冷卻使之達到所要求的溫度并計算各些行,人工變量從n+mne+m+1~m按行順序138計算機與應(yīng)用化學(xué)200421(換熱器的熱負荷輸岀各換熱器進、岀口溫度、熱容3913444kj/h燃料油燃燒值40806kj/kg,爐效益流率、熱負荷及整個網(wǎng)絡(luò)回收的熱量、冷、熱能量體取0.85,則節(jié)省燃料油為978kg/h,一年按8000小丶的用量等。時生產(chǎn)時間計算,年節(jié)油7824噸,節(jié)能效益763萬元/年。由此可見使用本軟件對換熱網(wǎng)絡(luò)進行優(yōu)化3換熱網(wǎng)絡(luò)分析實例分析可獲得很大的經(jīng)濟效益。將上述求解方法編制計算機程序,計算了多個3實例,對所提出的方法和程序進行了考核,下面給出其中一個實例以說明本方法的應(yīng)用情況。15sPⅠ換熱網(wǎng)絡(luò)有3股冷流、12股熱流C1、CC3三股冷流分別分成4股、2股2股分流進入換熱↓r她可也鹽435K網(wǎng)絡(luò)換熱要求見表1表1中原有網(wǎng)絡(luò)換后溫度列為實際運行數(shù)據(jù)C3物流只換熱到272℃。經(jīng)33過分析調(diào)優(yōu),求出各股分流的最佳流量和各換熱單元的最佳進出口溫度,使換熱網(wǎng)絡(luò)回收最大熱量l41得到圖3所示的改進后的換熱網(wǎng)絡(luò)。經(jīng)過優(yōu)化各股分流流量所得的最佳結(jié)果列入表2由結(jié)果分析可273.35知如果按線性規(guī)劃計算不優(yōu)化各分流流量所到的最大熱回收量Q-=20435901kj/h按非線性規(guī)劃計算優(yōu)化各分流流量后得到的最大熱回收量為220/7)2521211986638kj/h,年按8000小時生產(chǎn)時間計算年可節(jié)省燃料油1760噸,油價按975元/噸計算年節(jié)能效益為167.3萬元。如果與改進前的實際運行的換熱網(wǎng)絡(luò)相比C3改進前換后溫度為272℃優(yōu)化改進后為310℃,提高38℃,多回收熱量圖3改進后換熱網(wǎng)絡(luò)流程圖Fig, 3 Flow sheet of heat exchanger network after improvement表115s門1換熱網(wǎng)絡(luò)物流換熱要求Table 1 Requirement of streams for 15SPl problem序物流入口溫度原網(wǎng)絡(luò)換后溫度目標溫度流量比熱熱容流率物流名稱代號(k)kjhk (kjhk)脫前原油325.65406.15406,153186002,275672501脫后原油403.1597.15初底油>5733.0151常頂循381.15344.15341.152.3644211615383.1583.152.5650503.15413.15466252.5867常二中578.15496,153.0741563.15467.15333.1570002.674218720580.15491.15中國煤化工2.953963718HIo減四線CNMHGH,300008476H199.15383.151128702.8622323061200421(1)楊瑩等換熱網(wǎng)絡(luò)的分析表215SP1換熱網(wǎng)絡(luò)分析結(jié)果Table 2 Analysis results of heat exchanger for 15SPI problemK換熱器子系統(tǒng)414.91383.15325.6555.83200067,41l8I187.506353161.5012345678406,82316034.75181187.508232580,50381,15348,06325,65371,15211615,1153883.237001686,0010153883348.33406.15120606.53139801.5611254026.00563.15325.6542.6818720.0250144.394258818.00323060.53250144.390880698.00446.65414.91403.15422.8717.07200067.41322092.136351121.0063.3710.3316034.75322092.1313046309.00602.15463.37472.18322092.1328358l1537.37482.18472.1826.1763717.76322092.1316713.75H234593.10483.1084761.63513.15413.15403.15425.94395735.509020054.003.15441.64425.94444.69395735.507418507.00454.69395735,5015655742.00503,4523.85395735,505104833.5047.15493.15323060.534213313.00578.15530.36525.489213.61222874.00439673.1910650640.00554439673.192275241611.62554.82323060.53439673.1913254207.00559.45503.15493.15517.322.34194519.64452785.80952094.0063717.76452785.812725844.00620.15546.50523,36537,1546.8784761.63452785.816242693,00547,1冷卻器子系統(tǒng)406.82403.1370.91374.58316034.75316034.75159972.251.15211615.16211615.161462920.25429.5:413.15397.384761.634761.631390466.50348.333.15300.91120606.53120606.5330577.1318720.0846799.36390.06383.15350.91357.81323060.53323060.532230813.75453.15482.18420.912.2463717.7663717.761849596.2413.15393.15360.91380.9190200.5490200.541804010.75503.45503.15470.91471.2032,24222874.00222874.0065842,6511530.36526.35494.11222874.00874.00894233,631.熱回收量Qmx:211986624.00kj/h2.沒被冷流冷卻的熱流的熱負荷Qmn:13247694.00/h3.沒被熱流加熱的冷流的熱負荷4.換熱器的平均溫差Da:32.24K5.最小允許的接近溫度分析后所得的最佳參數(shù)可大大提高換熱網(wǎng)絡(luò)的熱回4結(jié)論收量可獲得巨大的經(jīng)濟效益。符號說明1)本文所建立的換熱網(wǎng)絡(luò)優(yōu)化分析的數(shù)學(xué)模n換熱網(wǎng)絡(luò)中換熱單元數(shù)目型正確可靠由此建立的求解方法行之有效經(jīng)實例t,m第;個單元冷物流的進、出口溫度考核計算獲得正確的結(jié)果ThH均的泄出口溫度中國煤化工(2)復(fù)合形法與線性規(guī)劃的單純形求解方法有mCNMHG熱器序號機地結(jié)合,成功地解決了換熱網(wǎng)絡(luò)的非線性規(guī)劃問sk下標,對冷流出口溫度有約束的換熱器序號題,與其他方法比較,成功率高,是一種好方法。ms熱流出口溫度有約束的換熱器數(shù)所編制的軟件可在工程研究、設(shè)計中應(yīng)用。mes冷流出口溫度有約束的換熱器數(shù)(3)經(jīng)過實例計算證明對換熱網(wǎng)絡(luò)進行優(yōu)化T,熱流和冷流溫度約束值r;下標,第i個熱流混合單元混合后進入另一個換熱單元的序號計算機與應(yīng)用化學(xué)200421(其入口溫度等于混合單元各分流混合后的溫度heat exchanger network synthesis using block decomposition and nonk;;下標,第i個熱流混合單元,第j股流來自的換熱單元序號linear optimization. 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