Analysis of a Looped Steam Pipe Network

Transcription

1 511 A publcaton of CHEMICAL ENGINEERING TRANSACTIONS VOL. 45, 2015 Guest Edtors: Petar Sabev Varbanov, Jří Jaroír Kleeš, Sharfah Rafdah Wan Alw, Jun Yow Yong, Xa Lu Copyrght 2015, AIIC Servz S.r.l., ISBN ; ISSN The Italan Assocaton of Checal Engneerng OI: /CET Analyss of a Looped Stea Ppe Network Shh-Han Wang, We-Jyun Wang, Cheng-Lang Chen* epartent of Checal Engneerng, Natonal Tawan Unversty, Tape 10617, Tawan, R.O.C CCL@ntu.edu.tw In ths work, we report on analyss of a looped stea ppe network wth ult-nput stea sources and ult-output background process snks. Hardy Cross ethod, whch was developed for looped water ppe network analyss, s adopted and odfed to deterne stea flow dstrbutons n all connectng ppes n the looped stea ppe network wth consderaton of the heat loss fro these ppes to the surroundngs and the pressure drop wthn the ppes. Then, pressure profle, teperature profle, as well as condensate are calculated and used to deterne stea flow path wthn the stea ppe network. Fnally, oveent of locatons of possble stagnaton ponts, where the stea flow rate s sgnfcantly saller than the noral operatng condtons, are dentfed n several network operatng scenaros. These analyses wll be deonstrated n a large-scale refnery n Tawan as a bass for optal operaton and plant retroft. Slar analyss wll be also appled on the typcal hgh pressure stea dstrbuton network n an ndustral coplex n Tawan. 1. Introducton Stea ppe networks play an portant role n transportng heat energy to process unts n checal ndustry, such as dstllaton coluns and theral crackng unts. Yet, because pressure drop and heat loss occur when stea flow through ppes, subcoolng phenoenon and condensaton ay take place at the stagnaton ponts, sectons where stea flowrate s sgnfcantly low. Moreover, the stagnaton ponts wll ove after operatng condtons of the network are changed. ue to poor qualty and nstablty of stea flow at stagnaton ponts, t s very dffcult to operate process unts near these ponts. ue to the above reasons, perforng stea network analyss at dfferent operatng states s crucal to ensure process safety. Accordngly, a nuber of researchers have nvestgated analyss of sngle ppelne. Idsnga et al. (1977) nvestgated the perforance of two-phase pressure drop correlatons for stea ppelnes. Probert et al. (1982) nvestgated nfluental factors contrbutng energy cost of transttng superheated stea n heat nsulated ppes. Baleck and Kruczek (1996) proposed an teratve algorth to sulate stea flow through ppe segents and fttngs. Vera and co-workers (García-Gutérrez et al., 2009) developed a nuercal odel for analyss of the stea network at the Los Azufres geotheral feld. Luo et al. (2012) proposed a hydraulc-theral odel and an teratve algorth to deterne stea flowrate n each ppe n a network. Gudo et al. (2013) nvestgated the perforance of cubc equatons of state and non-analytcal equatons of state n sulaton of carbon doxde ppelnes. Lug Raond (2014) studed the dynac phenoena n the ppelne transport of carbon doxde. However, looped network archtecture are preferred because of relablty ssues, especally n an ntegrated checal plant whch has a large nuber of nterconnected process unts. The ost coonly analyss ethods used to deterne ppe dscharges and nodal heads are the so-called Hardy Cross ethod (Cross, 1936), the Newton-Raphson ethod and the lnear theory ethod (Isaacs and Mlls, 1980). Manojlovć et al. (1994) proposed an algorth whch apples the Hardy Cross ethod to deterne optal daeters of all ppes n a looped gas ppe network. Brkć (2009) ade use of the orgnal Hardy Cross ethod and the proved sultaneous ethod to analyze natural gas dstrbuton networks. But, these ethods are not applcable to analyse looped stea networks wth copressble and non-sotheral flow. Accordng to our knowledge, the ethod for analysng such networks has never been proposed. That s the purpose of ths contrbuton. Please cte ths artcle as: Wang S.-H., Wang W.-J., Chen C.-L., 2015, Analyss of a looped stea ppe network, Checal Engneerng Transactons, 45, OI: /CET

2 512 Ths anuscrpt s organzed as follows: In Secton 2, the ethod for analyss of looped stea networks are presented. An exaple of network analyss s presented n Secton 3. Fnally, conclusons are drawn n Secton The Proposed odel for ppe network analyss In ths study, we proposed a odfed Hardy Cross ethod whch can be appled to analyze looped ppe networks wth copressble and non-sotheral stea flows. To begn wth, the followng quanttes are requred to be known for analyss: aeter, length L and roughness e of ppes. Abent teperature T e. Overall heat transfer coeffcent Pressure loss factor of fttngs ζ. Inlet stea teperature, pressure and ass flow rate at each stea source on the network. Outlet stea ass flow rate at each stea snk on the network. Followng assuptons are ade n the network analyss n ths work: There s no stea accuulaton wthn ppes. The aount of condensed water n the ppe network s very sall. So, exstence of condensed water does not affect physcal propertes of the stea flow. Speed of stea flows n the ppe network s saller than 0.3 Mach. There are no copressors and turbnes n the ppe network. 2.1 Mass balance at each node: The ass balance equaton can be wrtten as follows: n,total out, total where s the ass flowrate. 2.2 Head balance for each loop: If the operaton of a network reaches ts steady state, the su of head loss around a closed loop should be zero. Eq(2) s the orgnal head balance equaton of the Hardy Cross ethod (Cross, 1936). (1) All strea n loop k f L Q Q 0 (2) Yet, Eq(2) s not applcable to analyze stea network because flow of stea s copressble. Therefore, we use ass flowrate to substtute voluetrc ters Q n Eq(2) and nclude the head loss n fttngs. The odfed equaton can be wrtten n the followng: 8 24 g All strea n loop k f L 0 (3) where ρ s densty, f s frcton factor, g s gravty constant and ζ s pressure loss factor of fttngs. and f are the ean quanttes whch are calculated based on the average of stea teperatures and pressures at both ends of the ppe segent.

3 In general, Eq(3) s not possbly satsfed wth the ntal guess of the ass flow rates. Slar to the orgnal Hardy Cross ethod, we have to the apply correcton of, Δ. Therefore, the updated balance equaton can be wrtten as follows: 513 f L 8 ( ) 24 g k k All strea n loop k 0 (4) Then, we can obtan the correctve ter, Δ k (Eq(5)) va expandng Eq(4) and gnorng the second order of Δ k. k All strea n loop k 2 All strea n loop k 8 24 g 8 24 g f L f L (5) Updated values of can be obtaned by applyng the correctons of :, updated, old k for all stea n loopk (6) 2.3 Mass balance at each node: The procedure for analyss of looped stea networks s stated as follows: 1. Nuber all ppes, loops and nodes n the network. 2. Assue clockwse (or counter-clockwse) flow drecton n all loops as postve drecton. 3. Intal guess of ppe dscharges: Assue nu nuber of arbtrary ppe dscharges and use the contnuty equaton to deterne dscharges other ppes. 4. Assue arbtrary unfor teperature and pressure n the entre network. 5. Use the ntal value of ppe dscharges, teperature and pressure to deterne the average of densty and frcton factor. 6. Use Eq(5) to obtan the correcton of ppe dscharge Δ k. 7. Apply the correcton of ppe dscharge to every ppe n the network. 8. Repeat Step 5 to Step 7 untl the correcton of ppe dscharge s saller than the defned convergence crteron? (Ex: 0.01 %). 9. Select the node wth axu pressure as the startng pont and use oentu balance to calculate pressure at reanng nodes. 10. Use energy balance to calculate teperature and aount of condensed water at each node. 11. Repeat Step 5 to Step 10 untl correctons of pressure, teperature and ppe dscharge are saller than convergence crteron. 12. The flow dstrbuton and flow patter of the network are obtaned. The procedures of looped stea networks analyss are suarzed n Fgure 1.

4 514 Input data and paraeters Nuber all ppes, nodes, loops and nput ponts Set clockwse flow drecton as postve drecton Assue an unfor pressure and teperature ntally Set soe ppe dscharges arbtrarly and use ass balance to calculate the reanng ppe flow rate Calculate all needed propertes, e.g., densty, vscosty, Reynolds nuber, frcton factor Calculate k n each loop Add each k to each ppe whch belongs to loop k sultaneously, to get revsed ppe flow rate Is k sall enough between teratons? Yes Calculate pressure and teperature at each node Is P, T, sall enough for each node and loop between teratons? Yes Soluton No No Update No Cond. occurs? Yes Update T and P Update T, P and nodal flowrate Fgure 1: Procedures of stea network analyss 3. An llustratve exaple In ths secton, we apply the proposed analyss ethod to one network exaple. Ths network has totally sx ppes, fve nodes wth two sources and three snks and two loops. Layout of ths network s shown n Fgure 2. Paraeters for analyss are suarzed n Table 1. The overall heat transfer coeffcent s calculated based on the nner daeter of ppe. Results of analyss are suarzed n Table 2 and flow pattern of the network s shown n Fgure 3. The results show that the studed stea network does not have stagnaton pont. However, the flow rates n ppes 2 and 5 are uch hgher than other ppes. Whereas the flow rate n ppe 6 s qute sall. Table 1: Paraeters for network analyss Inner daeter of all ppes () Thckness of ppe wall () Thckness of heat nsulaton () Overall heat transfer coeffcent (W/( 2 *K)) Abent Teperature (K) Roughness () *10-5

5 515 1 <2> L 2 = = kg/s 3 <3> L 3 = = 150 <1> L 1 = = 150 [1] <6> L 6 = = 150 [2] 5 <4> L 4 = = kg/s 2 <5> L 5 = = kg/s <1> Ppe no. <1 Node no. [1] Loop no. Fgure 2: Layout of the network Input kg/s T = 650 Ka0000 P = Pa 2 kg/s <2> 1 Q 2 = kg/s 3 <3> Q 3 = kg/s <1> Q 1 = kg/s [1] <6> L 6 = = 150 [2] 5 4 kg/s Input kg/s T = 650 Ka0000 P = Pa 2 <5> 4 Q 5 = kg/s 6 kg/s <4> Q 4 = kg/s <1> Ppe no. <1 Node no. [1] Loop no. Flow drecton Fgure 3: Flow pattern of the network Table 2: Results of the llustrated network analyss Ppe No. Ppe scharge (kg/s) Node No. Nodal Tep. (K) Nodal Pressure (MPa) Conclusons In ths work, a odfed Hardy Cross ethod for analyss of looped stea networks s proposed. Ths ethod can be used to predct responses of ppe networks wth dfferent operatng scenaros. The results are hghly valuable to optze network operaton and prevent possble accdents. The analyss s perfored n a large scale refnery n Tawan n an on-gong project.

6 516 Noenclature f L T P ζ ρ g Q ass flowrate nner ppe daeter frcton factor length of ppes teperature pressure pressure loss factor of fttngs densty gravty constant voluetrc flowrate References Idsnga W., Todreas N., Bowrng R., 1977, An assessent of two-phase pressure drop correlatons for stea-water systes, Internatonal Journal of Multphase Flow, 3, Probert S.., Yeung S.., Chu C.Y., 1982, Optzng the perforance of nternally nsulated ppelnes for conveyng superheated stea, Appled Energy, 12, Baleck R.A., Kruczek T., 1996, Frctonal, datheral flow of stea n a ppelne, Checal Engneerng Scence, 51, García-Gutérrez A., Martínez-Estrella J.I., Hernández-Ochoa A.F., Vera M.P., Mendoza-Covarrubas A.M., Ruz-Leus A., 2009, evelopent of a nuercal hydraulc odel of the Los Azufres stea ppelne network, Geothercs, 38, Luo X., Yuan M., Wang H., Ja Y., Wu F., 2012, On stea ppe network odelng and flow rate calculaton, Proceda Engneerng, 29, Mazzoccol M., Gudo G.., Boso B., Arato E., Pellegrn L.A., 2013, CO 2-xture propertes for ppelne transportaton n CCS process, Checal Engneerng Transactons, 32, Raond L., 2014, CO 2 transportaton wth ppelnes odel analyss for steady, dynac and relef sulaton, Checal Engneerng Transactons, 36, Cross H., 1936, Analyss of flow n networks of conduts or conductors, Unversty of Illnos, Bulletn No 286, Isaacs L.T., Mlls K.G., 1980, Lnear theory for ppe network analyss, Journal of Hydraulc vson, 106, Manojlovć V., Arsenovć M., Pajovć V., 1994, Optzed desgn of a gas-dstrbuton ppelne network, Appled Energy, 48, Brkć., 2009, An proveent of Hardy Cross ethod appled on looped spatal natural gas dstrbuton networks, Appled Energy, 86,