CONTROL LOOP CONFIGURATION AND ECO- EFFICIENCY

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1 CONTROL LOOP CONFIGURATION AND ECO- EFFICIENCY M.T. Munr, W. Yu and B.R. Young * Chemcal and Materals Engneerng Department The Unversty of Auckland Auckland, New Zealand Abstract Snce the eco-effcences of all ndustral processes/plants have become more and more mportant, engneers need to fnd a way to ntegrate loop confguraton and measurements of eco-effcency. A new measure of ecoeffcency for loop confguraton was developed, the exergy effcency factor. The exergy effcency factor s based on the thermodynamc concept of exergy whch can be used to analyze a process n terms of ts effcency. The combnaton of the Relatve Gan Array (RGA) and the exergy effcency factor wll help gude the process desgner to reach the optmal desgn wth low operatng cost. The proposed method s valdated by dynamc smulaton. Keywords Control loop confguraton, Eco-effcency, Dynamc exergy effcency. Introducton Control loop confguraton or par selecton focuses on selectng the best scheme for parng manpulated and led varables. Several common technques: Relatve gan array (RGA), Nederlnsk ndex (NI), Sngular value decomposton (SVD) and Decouplng have been developed for loop confguraton (Seborg et al. 1989; Svrcek et al. 2006). Based on these common technques, many researchers have developed more comprehensve technques for assgnng loops on more complex processes. These technques provde a relable support for ndustry to guarantee the qualty of products. Now days, n the wake of the energy crss and global warmng loop confguraton can not only focus on loop analyss technques alone such as loop stablty analyss and consderaton of the qualty of the ler varable, but must also nclude energy cost and envronment mpact. A new tool must be developed to ntegrate above two aspects for process and economcs/sustanablty. In most loops, exergy can play an mportant role n ths new tool snce t can be used for determnng the exergetc effcency and sustanablty of a process (Dncer 2002). For example, envronmental mpacts can be mnmzed by reducng exergy losses and by effcent use of exergy (Rosen and Dncer 1997; Rosen and Dncer 1999). The use of thermodynamc propertes lke exergy has potental to be used for the development of process structures. Luyben et al. (1998) added an appendx n hs book whch acts as a basc framework for the development of a dynamc exergy balance for process evaluaton. The Relatve Exergy Array (REA) was developed based on analyzng the exergy for the confguraton wthn the process desgn (Montelongo- Luna et al. 2009; 2011). Some research has also been done on process effects on entropy producton (Alonso et al. 2002; Ydste 2002; Martn et al. 2005). The REA s the extenson of the RGA nto the exergy doman. The REA s defned by placng the exergy * b.young@auckland.ac.nz

2 thermodynamc property n the place of gan n the RGA analyss. The REA may provde a deeper nsght nto process structure nteractons and measurement of exergetc effcency and can be used for quck comparson between several process/ structure canddates. REA calculaton usng a commercal smulator (VMGSm) has been developed (Munr et al. 2010; Munr et al. 2011).The effect of recycle on the REA analyss was studed by Munr et al.(2011). If RGA and REA conflct then fnal selecton should be based on RGA. The REA evaluates the eco-effcency only wthn the scope of the loops studed; t cannot provde the eco-effcency of the whole unt or plant. In ths paper, we wll extend the eco-effcency of the loop confguraton nto the whole unt/process or even plant. A new measure of eco-effcency, exergy effcency factor, s proposed. Ths manuscrpt s organzed as follows. After ths general ntroducton, the concept of eco-effcency s ntroduced, the relevant exergy defntons are dscussed and the exergy effcency factor s proposed. Then, the proposed method s mplemented for two smulaton examples. Fnally, the results are dscussed and conclusons are made n the summary. Eco-effcency Accordng to the World Busness Councl for Sustanable Development (WBCSD) defnton, ecoeffcency s acheved through the delvery of "compettvely prced goods and servces that satsfy human needs and brng qualty of lfe whle progressvely reducng envronmental mpacts of goods and resource ntensty throughout the entre lfe-cycle to a level at least n lne wth the Earth's estmated carryng capacty." Ths concept descrbes a vson for the producton of economcally valuable goods and servces whle reducng the ecologcal mpacts of producton. In other words ecoeffcency means producng more wth less. When applyng the concept of eco-effcency to loop confguraton, we need to develop a method whch can help engneers select the manpulated varables whch acheve the best products wth the lowest energy cost. In every chemcal process there are some materals comng n or gong out. Smlarly, every process needs some energy to perform ts work and/or the process rejects energy to the surroundngs. So the materal and energy balances of the process are generally used to evaluate the effcency of the process at the process desgn stage. For energy balance calculatons chemcal engneers mostly only focus on the 1st Law of Thermodynamcs (Hmmelblau and Rggs 2004). However ths approach may not fully reflect realstc energy effcency. The 2nd Law of the thermodynamcs must be ncluded to provde a more realstc understandng of energy usage and wastage (Denbgh 1956). Thermodynamc laws (1 st and 2 nd ) may gve an dea about process effcency, energy loss, work done, requred work and entropy producton. For energy effcency of a process, nputs, outputs and losses are defned n terms of energy (Smth and Ness. 2005).The combnaton of the 1 st and 2 nd laws of thermodynamcs gves rse to the concept of exergy whch s the basc measure of eco-effcency. Exergy s the maxmum possble amount of work whch can be drawn from a materal stream when t nteracts only wth the envronment as t comes from ts ntal state to the fnal dead state (Denbgh 1956; Kotas 1985). Exergy A general thermodynamc process s shown n Fgure 1. The process has many arbtrary materal streams comng from and gong out of the process boundary. The process has ts own temperature (T), pressure (P) and composton (Z). The process s also heated from dfferent heatng sources at dfferent temperatures T delverng dfferent amounts of heat q. The process produces some shaft work (W) and delvers t to the envronment wth fxed values of temperature, pressure and composton (T 0, P 0 and Z 0 ). F (Flow In) Thermal energy reservors q 1 q 2 q 3 T 1 T 2 T 3 Control regon T, P, Z Shaft work W T0, P0, Z0 D e (Flow out) Fgure 1: A general thermodynamc process The change n nternal energy ( U) of the general thermodynamc system shown n Fgure 1 s due to the addton of energy nputs (q ) and work done (W). Accordng to the 1st Law of Thermodynamcs, nternal energy change ( U) can be expressed as, U q q P V W (1) 0 0 where q 0 = heat provded to the system, q = all other heat effects, P0 V = work done n dsplacng the atmosphere at constant pressure, and W = all other work terms. Accordng to the 2nd law of thermodynamcs, the total entropy created, σ, can be expressed as, S S S (2) 0 0

3 where S = Entropy, S 0 = Change n entropy outsde the process and S = Change n entropy nsde the process. The heatng medum s a heat reservor at a constant temperature and ts change n entropy s S 0. S Q / T (3) From Equatons (1), (2) and (3), we can obtan the followng thermodynamc expresson for the process n Fgure 1, W q T S T U P V T S (4) where W q T S 0 performed on the process and due to rreversblty denotes the total work T denotes the energy loss Exergy s the maxmum possble amount of work whch can be drawn from a materal stream when t nteracts only wth the envronment and t comes from ts ntal state to the fnal dead state (Denbgh 1956; Kotas 1985). At the dead state the materal stream s n thermal, mechancal and chemcal equlbrum wth the envronment. Snce exergy accounts for the qualty of energy, thus t can be used as a measure to evaluate the eco-effcency for a process desgn. A process s called eco-effcent f t uses a relatvely small amount of energy or destructon of exergy s low. The calculaton of the physcal exergy change of the thermodynamc process n Fgure 1 can be obtaned from Equaton (4) as, 0 Bphys U P0 V T0 S (5) Because the thermodynamc process composton Z and the envronmental composton Z0 n Fgure 1 are desgned for dfferent work potentals, the total exergy of the materal stream wll also change. The total exergy, ncludng the three components: physcal exergy, chemcal exergy and exergy due to mxng, s defned as (Hndernk et al. 1996), Btotal Bphys Bchem mxb (6) The detaled defntons of chemcal exergy, B chem, and exergy change due to mxng, mx B, are provded n (Hndernk et al. 1996). Based on an understandng of the total exergy of each materal stream n and out of the thermodynamc process, t s possble that engneers can buld an eco-effcent process whch s ecologcal and economcal. The total exergy calculaton n Equaton (6) s relatvely smple and only needs easly obtanable thermodynamc data. Ths calculaton requres data such as the Gbbs energy formaton for the calculaton of standard chemcal exerges. The Gbbs energy formaton data can be obtaned from dfferent sources lke thermodynamc databanks or process smulators but specal attenton must be pad to the consstency of ths data. However, even n the presence of many commercal chemcal process smulators, exergy calculaton s not easy or straght forward n practce. The automaton of exergy calculaton was done by usng a commercal smulator (Aspen HYSYS) and an open source (Sm42) (Montelongo-Luna et al. 2007). An ntegrated Vsual Basc (VB) program and Graphcal User Interface (GUI) was recently developed for exergy calculaton (Munr et al. 2010). Eco-effcency factor of the Manpulated Varable In the above secton, we ntroduced the dea that exergy can be used to measure the energy changes of one process/unt/plant. Exergetc effcency was defned as the rato of the exergy gong out to the exergy gong nto a process as shown n Equaton (7) (Sazargut et al. 1988). B / B (7) out n where = Exergetc effcency, B out = Total exergy gong out of a process and B = Total exergy comng n to a process. n The rato can be used to measure the exergy effcency of a process whch s equvalent to eco-effcency. A general process for exergetc effcency calculaton s shown n Fgure 2. Ths general process s a porton of the loop between the manpulated and the varable. u j, B In Process y, B Out Equaton (7) ncludes the exergy effcency for the whole process; however t does not provde any nformaton about how the loop confguraton affects ths exergy effcency. In ths paper we propose a new measure, eco-effcency factor, whch connects the loop confguraton to the eco-effcency. The exergy effcency factor for a par (u j, y ), s defned as, u j j ( Bout Bn ) (8) y where Fgure 2: A general process u j denotes a step change of the MV, u j, y denotes a response n the CV, y caused by a step change of the MV, u j, and Bout and Bn represent the exergy dfferences caused by the MV step change for exergy out

4 and exergy n respectvely. For example, f 21 s less than 22, t means that for the same amount of CV, change, y 2 usng MV, u 1, wll cause less exergy than usng MV, u 2. The fnal nterpretaton s that par (u 1, y 2 ) s more eco-effcent than par (u 2, y 2 ). Usually loop confguraton s determned by technques such as RGA and NI. The result s often that several canddate loop confguratons can be used. Our new eco-effcent factor can be used to select the best loop confguraton among the canddates n the sense of ecoeffcency. Valdaton of Eco-effcency factor Dynamc smulaton s the best way to valdate the proposed eco-effcency factor. By recordng the exergy consumptons of several confguratons, we can dentfy the most eco-effcent confguraton and compare the dynamc result to the result from the ecoeffcency factor. Dynamc exergy versus tme can be approxmated by several exergy calculatons at dfferent condtons durng the dynamc response of a process. The exergy values of the process dynamc response at dfferent tme ntervals are calculated. As chemcal smulators stll do not have the ablty to drectly calculate and dsplay the total exergy of a materal stream, these smulators cannot calculate exergy at every pont versus tme automatcally. Smulators such as HYSYS and VMGSm can only calculate steady state exergy values at gven process condtons. For dynamc exergy versus tme, dfferent ponts are selected durng the process dynamc response due to step nput dsturbances. The selecton of calculaton ponts depend on the process response. Then the exergy values are calculated on those selected ponts durng the dynamc process response. Exergy values at dfferent ponts are calculated wth the procedure developed n Munr et al. (2010). Then those exergy ponts are used to approxmate the dynamc exergy response versus tme. Case Study For ths case study, a dstllaton column wth dual composton s selected. A schematc of ths dstllaton column s shown n Fgure 3. VMGSm wth the NRTL actvty thermodynamc model s used for ths smulaton. Table 1 summarzes the feed condtons and the dstllaton column specfcatons. The compostons at the top and bottom of the dstllaton column, x D and x B, are the led varables. For two-pont composton of ths dstllaton column three basc confguratons: DV, LV and LB are the possble canddates. For example, n the LV confguraton, L (Reflux rate) s used to the composton of the top product, x D and V (Bol-up rate) s used to the composton of the bottom product, x B (Svrcek et al. 2006). Feed Reflux (L) Column Bol-up (V) Condenser Condenser duty Accumulator Dstllate (D) Reboler duty (Qr) Bottoms (B) Fgure 3: Dstllaton column schematc Table 1: Feed and dstllaton column specfcatons Feed Feed Composton Flow (kmole/hr) 152 E- oxde (Mole fracton) Tray specfcatons Water (Mole fracton) 0.31 Dameter (m) 1.5 E-glycol (Mole fracton) 0.67 Wer heght (m) 0.5 Pressure (kpa) 110 Wer length (m) 1.2 Temperature ( o C) 65 Column specfcatons Total number of stages 10 Feed stage Condenser type Table 2: Control parngs for the three confguratons Confguraton u 1 y 1 u 2 y 2 5 th Partal Column overhead pressure (kpa) 100 Column reboler pressure (kpa) 105 DV D x d V x b LV L x d V x b LB L x d B x b

5 Exergy ( x10 5 Kw) Exergy ( x10 5 kw) The RGA values for the three basc confguratons calculated from the gan matrces are, LV DV LB These RGA results show that the leadng dagonal elements of the LB and LV confguratons are postve and can be further selected for evaluaton of the exergy effcency of the process. The DV confguraton s not further selected as ts leadng dagonal elements are sgnfcantly less than 1 and negatve whch are not favorable. Its off-dagonal elements are postve and close to 1, but the parng of off-dagonal elements ntroduce a sgnfcant amount of dead tme n the process whch s not favorable. After selectng the LB and LV confguratons, we wll use the proposed eco-effcency factor to evaluate the effect of each par on the overall exergetc effcency of the process. The eco-effcency factor of each par of MV and CV s lsted n Table 3. A par whch gves lower exergy effcency factor s favorable and vce versa. Table 3: Eco-effcency factor Control Pars EEF (kw) (L, x D ) 36.5E7 (V, x B ) 33.7E5 (B, x B ) 22.6E5 From Table 3, the par (L, x D ) wll use the most exergy and be the least eco-effcent par, and the par (B, x B ) s the most eco-effcent par. For lng one CV, x B, f we use B as the MV, t wll save 33% exergy comparng to use V as the MV. After buldng the dynamc model of ths case study, we mplemented the PI lers for the two (LB and LV) confguratons wth nventory s. Zegler Nchols open loop tunng method s used for ths smulaton, the PI ler parameters are lsted n Table 4. For each confguraton, the set ponts of CVs x D and x B are changed at the same tme and by the same amount. The dynamc exerges n and out of ths dstllaton column are approxmated by the proposed method. Fgure 4 and 5 show the dynamc exerges for the two confguratons LV and LB respectvely. The total exerges for the 70 mn tme perod are lsted n Table 5. Table 4: PI Controllers for dynamc smulaton Control loops Feed flow Overhead pressure Condenser level Reboler level x D Composton x B Composton LV confguraton LB confguraton K c T (mn) K c T (mn) Tme (mns) Total Exergy In Total Exergy Out Fgure 4: Varaton of Exergy In and Exergy Out due to composton set pont changes for the LV confguraton Total Exergy In Total Exergy Out Tme (mn) Fgure 5: Varaton of Exergy In and Exergy Out due to composton set pont changes for the LB confguraton

6 Table 5: Exergy used by two confguratons LV and LB Control Confguraton LV (10 4 kw) LB (10 4 kw) Total Exergy n Total Exergy out Total destroyed Exergy From Table 5, the total destroyed exergy for the whole operaton s kw under the LB confguraton. Compared to the LV confguraton, LB can save 38% exergy. Ths concluson agrees wth the result from the eco-effcency factor. The percentages of the exergy savng from two methods are qute smlar, whch ndcates that the EER can provde a relable gude to selectng the more eco-effcent confguraton. Conclusons A new measure, eco-effcency factor, for ntegratng the loop confguraton and eco-effcency s proposed n ths paper. The smulaton result shows that the eco-effcency factor can provde a qualtatve and quanttatve measure to gude engneers to select the most eco-effcent confguraton. Acknowledgments The authors would lke to acknowledge the support of the Industral Informaton and Control Centre (I 2 C 2 ), Chemcal and materals engneerng department, Faculty of Engneerng, the Unversty of Auckland, New Zealand. References Alonso, A. A., B. E. Ydste and J. R. Banga (2002). "From rreversble thermodynamcs to a robust theory for dstrbuted process systems." Journal of Process Control 12(4): Denbgh, K. G. (1956). "The second-law effcency of chemcal processes." Chemcal Engneerng Scence 6(1): 1-9. Dncer, I. (2002). "The role of exergy n energy polcy makng." Energy Polcy 30: Hndernk, A. P., F. P. J. M. Kerkhof, A. B. K. Le, et al. (1996). "Exergy analyss wth a flowsheetng smulator - I. Theory; calculatng exerges of materal streams." Chemcal Engneerng Scence 51(20): Kotas, T. J. (1985). The exergy method of thermal plant analyss. London, Butterworths. Luyben, W. L., B. D. Tyreus. and M. L. Luyben. (1998). Plantwde Process Control. New York, McGraw-Hll. Martn, R., G.-O. Vaney and B. E. Ydste (2005). "Passvty based of transport reacton systems." AIChE Journal 51(12): Montelongo-Luna, J. M., W. Y. Svrcek and B. R. Young (2007). "An exergy calculator tool for process smulaton." Asa-Pacfc Journal of Chemcal Engneerng 2(5): Montelongo-Luna, J. M., W. Y. Svrcek and B. R. Young (2009). The Relatve Exergy Array - A tool for ntegrated process desgn and Chemeca Perth, Australa. Montelongo-Luna, J. M., W. Y. Svrcek and B. R. Young (2011). "The relatve exergy array a new measure for nteractons n process desgn and." The Canadan Journal of Chemcal Engneerng 89(3): Munr, M. T., J. Chen and B. R. Young (2010). A computer program to calculate the stream exergy usng the vsual basc graphcal nterface. Chemca Adelade, Australa. Munr, M. T., W. Yu and B. R. Yong (2011). "Recycle effect on the Relatve Exergy Array." Chemcal Engneerng Research and Desgn: (n press). Munr, M. T., W. Yu and B. R. Young (2011). Determnaton of Plant-wde Control Loop Confguraton and Eco- Effcency. Plant Wde Control: Recent Developments and Applcatons G. P. Rangaah and V. Karwala, John Wley & Sons (accepted). Rosen, M. A. and I. Dncer (1997). "On exergy and envronmental mpact." Internatonal Journal of Energy Research 21: Rosen, M. A. and I. Dncer (1999). "Exergy analyss of waste emssons." Internatonal Journal of Energy Research 23: Sazargut, J., D. R. Morrs and F. R. Steward (1988). Exergy analyss of thermal chemcal and metallurgcal processes. New York, Hemsphere Publshng. Seborg, D. E., T. F. Edgar and D. A. Mellchamp (1989). Process Dynamcs and Cotrol. New York, John Wley & Sons. Smth, J. M. and H. C. V. Ness. (2005). Introducton to Chemcal Engneerng Thermodynamcs. New York, McGraw- Hll. Svrcek, W. Y., D. P. Mahoney and B. R. Young (2006). A Real- Tme Approach to Process Control. Chchester, John Wley & Sons. Ydste, B. E. (2002). "Passvty based va the second law." Computers & Chemcal Engneerng 26(7-8):