Proceedngs of the 1 st Annual Gas Processng Symposum H. Alfadala, G.V. Rex Reklats and M.M. El-Halwag (Edtors) 2009 Elsever B.V. All rghts reserved. 1 Dynamc optmzaton of the LNG value chan Bjarne A. Foss a and Ivar J. Halvorsen b a NTNU, Department of Engneerng Cybernetcs N-7491 Trondhem, Norway b SINTEF ICT, Appled Cybernetcs, N-7465 Trondhem, Norway Abstract In operaton of a large LNG processng plant there wll be uncertantes related to plannng and realzaton of an optmal operaton strategy. Results show the mportance of ncludng the whole producton chan n the optmzaton. For a test scenaro where we look at the event of delayed shp arrval, ths gves lower losses than a normal approach where the upstream part of the system and the LNG process plant are optmzed ndvdually. The system s modeled by smple models of each man component startng at the wells and near-well regon and endng wth the export tanks for LNG, LPG and condensate. These proxy models can be regarded as frst order approxmatons of the real system. The ndvdual models are nonlnear, some are statc and others are dynamc models. The models have been coarsely valdated usng a hghfdelty smulator of the value chan at the Snøhvt LNG plant. Use of these qute smple models combned wth model-based optmzaton offers and nterestng and feasble approach to optmze producton n case of varous events that requre readjustment of the producton plannng. Keywords: Producton chan, LNG, smplfed models, optmzaton 1. Introducton Optmal operaton of large LNG processng plants may requre a holstc vew of the value chan. Ths s mportant f the LNG plant s tghtly connected to an upstream producton system and/or a downstream consumer. Present ndustral practce typcally takes a slo approach n the sense that one part of the supply chan s treated qute separate from other parts. Ths s pronounced n the upstream area where applcatons for optmally allocatng well producton nclude well models as well as models for some ppelne collecton system. The downstream boundary condton s typcally a constant pressure n a 1 st stage separator. Smlarly model-based optmzers for the separaton plant do not nclude models of the upstream part. Instead nformaton from the upstream part s passed as an exogenous varable ncludng flow rates, pressure and composton to the downstream optmzer. Ths mples that the nlet separator functons as a dvdng wall between the two optmzers even though the two subsystems mght be tghtly connected. An example of the latter arses f part of the gas output from the separaton plant s fed back nto the upstream system through gas-lft wells or gas njectors. There are many reasons for ths slo-lke stuaton. Dfferent parts of the supply chan recrut people wth dfferent backgrounds and they use dfferent tools for optmzaton. Ths lmts ntegraton even n stuatons where ntegraton has an obvous potental.
2 Foss and Halvorsen We study how model-based optmzaton can be used to fnd an optmal operaton strategy n the presence of unexpected operatonal events focusng on delayed arrval tmes for shps exportng stored products. In partcular the potental of combnng upstream producton system wth the downstream process plant nto one optmzaton problem and the use of smple models s explored. The system we study s a semrealstc model of the producton chan of StatolHydro s Snøhvt plant n Hammerfest, close to Norway s North Cape. The wells are stuated about 120 km from shore, and gas condensate s transported to the processng plant n Hammerfest through a multphase ppelne drven by the well pressure only. In addton to the central lqufacton unt, the plant conssts of gas pretreatment unts, a gas-fred power plant, a CO 2 separaton unt and storage tanks. LNG and condensate products are shpped to customers worldwde. It may be noted that CO 2 s sequestered n an aqufer. A stylstc vew of the plant s shown n Fg.1. Fgure 1: A stylstc vew of the Snøhvt producton chan (Dahl, 2007) The paper frst places the proposed method nto context by relatng t nto a wellestablshed process control herarchy. Subsequently the modelng approach and the optmzaton approach are presented. Thereafter a plausble test scenaro s descrbed together wth smulated results. The paper ends wth a dscusson and some conclusons. Page constrant lmts the depth of the presentaton. References are therefore gven for readers who seek more detaled nformaton on the method and results. 2. A process control herarchy The Snøhvt reservor flud s extracted subsea, transported n multphase ppelnes, refned and lquefed, stored, shpped, regasfed, stored, transported through some gas ppelne network and before t fnally can be used for heatng or as raw materal. Not only s the chan long and the transport methods vared, there are also many mportant decsons to be made by partners regardng and related to marked, prcng, stockng, producton level and producton securty. Some supply chans are drectly connected
Dynamc optmzaton of the LNG value chan 3 (lke natural gas used n fertlzer producton), others are more decoupled (lke the consumpton of electrcty produced at a gas power plant). Hence, not all parts are equally mportant to nclude n a supply chan. There are dfferent methods and applcatons for managng supply chans. We use the well establshed process control herarchy (see e.g. Backx, Bosgra and Marquardt, 2000) as a startng pont keepng n mnd that the process plant s n turn only a part of a larger supply chan, see also Fg.2. The levels are: Regulatory control: The low level control of processes are essental for keepng the plant stable and well functonng. Ths level usually conssts of conventonal PIDcontrollers. Supervsory control: Ths layer usually handles unts and may be based on manual adjustment of the regulatory layer controller setponts or model predctve control (MPC). Local optmzaton: Adjust targets to mantan close to optmal operaton under changng condtons. Ths layer s often based on real tme optmzaton (RTO) wth a model ftted to real tme data. Ste-wde optmzaton: For large plants, there wll usually be a plant wde RTO level, coordnatng sectons and unts. Schedulng and plannng Plannng s closely connected to the whole supply chan. The plannng level can agan be subdvded nto long-term (e.g. nvestment decsons), md-term (e.g. season plannng, sales contracts, mantenance plannng), and short-term plans. The latter ncludes settng targets for the ste-wde optmzaton, handlng dscrete operatons lke shp arrvals and loadng and re-plannng n case of unexpected events. Fgure 2. Control herarchy The focus n ths paper s the connecton between short-term plannng and ste-wde optmzaton. 3. LNG plant modelng approach The choce of model complexty s crtcal for the success of a model-based optmzaton. On the one hand the model must be accurate n the sense that optmzaton provdes reasonable results. On the other hand the model must be smple, or at least
4 Foss and Halvorsen computatonally effcent, such that the optmzaton problem can be solved wthn the tme constrants at hand. 3.1 Model structure Our approach s to model the system usng a modular structure wth smple models of each man component startng at the wells and near-well regon, and endng wth the export tanks for LNG, LPG and condensate. More precsely the modules nclude: wells, ppelne, slug catcher, condensate column, condensate tank, CO 2 -separator, LNG and LPG column, gas turbne, LNG and LPG coolng compressors, N 2 separator, LNG tank, and LPG tank, see also Fg.1. Some auxlary systems lke the floe assurance system s not ncluded n the model. The complete model can be vewed as a frst order approxmaton of the real system. The ndvdual models are nonlnear, some are statc and others are dynamc models. The models have been coarsely valdated usng a hgh-fdelty smulator of the value chan at the Snøhvt plant (Dahl, 2007). The smulaton model was created to solve some specfc optmzaton scenaros. Choce of producton strategy when export shps arrve late. Choce of producton strategy when one or more wells unexpectedly shuts down. These are both mportant and plausble scenaros, and producton strateges are chosen so as to mnmze loss n proft compared to the nomnal case. Ths s almost the same as fulfllng future contracts whle mnmzng the plant s operatonal costs lke coolngand electrcty use. 3.2 Model components We assume that t s possble to descrbe plant performance n a meanngful way wthout explctly ncludng detaled pressure-dynamcs. Hence, t s possble to solve the model sequentally startng wth the wells, contnung wth the multphase ppelne, the slug catcher and endng wth the storage tanks as depcted n Fg.1. Ths mples that the whole model can be solved very effcently. In the real plant there are several recycle flows. In the model ths s avoded by operatng wth perfect splts and by aggregatng cost and delays of these recycle flows nto the bgger unts. It s assumed that the aggregated plant model captures these plant dynamcs wth suffcent accuracy wthout ncludng complex recycle flows and mperfect splts. As a sde remark these dynamcs are very mportant to ensure qualty and safety under producton, but do not nfluence the overall dynamcs sgnfcantly. All model components use statc models, except the multphase ppelne, the slug catcher and the storage tanks. The ppelne dynamcs are sgnfcant n some cases snce ts settlng tme s about 10 hours. Instead of resortng to a complex multphase flow model, the ppelne model s a smple 2 nd order system whch accounts for the fact that lqud holdup vares wth the flow rate and t also ncorporates the man ppelne dynamcs.
Dynamc optmzaton of the LNG value chan 5 The decson varables, or control nputs, n the complete model are: The gas condensate flow rate from each wells (9 control nputs). The amount of energy produced n the gas turbne (1 control nput). The gas and condensate output flow rates from the slug catcher (2 control nputs). Export flow rates of LNG, LPG and condensate, respectvely, to approprate shps (3 control nputs). The mass flow whch s tracked by the model s composed of 8 dfferent components. These components are CO 2, N 2, methane, ethane, propane, butane, condensate (C 5+ ) and water. Some components have been neglected; our hypothess beng that t does not reduce the qualty of our results. The complete model ncludes mass component flow rates n and out of each module, and energy consumpton, f applcable, n each component. Some modules lke the LNG and LPG coolng compressors consume a sgnfcant amount of electrcal energy. Detaled nformaton can be found n (Dahl 2007). 3.3 Implementaton The model s mplemented usng MatLAB. Each component has the same nputoutput structure gven by W W,, W, E unt ( t, U, W ) out 1,, out 2, outn, n, out1, E are the component-based output mass flow rate, and consumed electrc and n, U, Wn, refer to the number of output streams, W, heat energy durng a tme perod. decson varables and the component-based nput mass flow rate, respectvely. t defnes the smulaton tme perod. 4. The optmzaton problem The optmzaton problem s formulated so as to mnmze some cost functon on a predefned future tme horzon, typcally 1-2 weeks. The tme axs s dscretzed, typcally wth a step sze of 3-6 hours. The decson varables may vary on the predcton horzon, thereby ncreasng the dmenson of the decson space consderably. To elaborate, lettng 15 decson varables, as defned n secton 3.2, vary every 6 hours on a one week predcton horzon provdes us wth a 420 decson varables. The mathematcal optmzaton problem conssts of three parts; an objectve functon, the model and constrants. The objectve functon provdes a quanttatve measure of the cost ncurred by reducng producton, compared to full capacty, as t wll be assumed that there s no market constrant. The model of the producton chan descrbed earler connects the whole system, n partcular t couples the decson varables and the varables that defne the cost functon. Fnally, the mathematcal optmzaton problem ncludes a number of constrants, manly capacty constrants n the ndvdual components along the producton chan. Due to page constrants we refer to Dahl (2007) for a comprehensve mathematcal descrpton.
6 Foss and Halvorsen The optmzaton problem we are left wth s a nonlnear program whch s solved usng a SQP-lke algorthm, see e.g. Nocedal and Wrght (2006). An alternatve approach s to use a mxed nteger optmzaton formulaton combned wth pecewse lnear models as by Tomasgard et.al. 2007 and Mdthun 2007. Common for both approaches s that models for the whole value chan are used, and that the formulaton of models have to be somewhat adjusted to ft the optmzaton formulaton. 5. Test scenaro and results To evaluate a model-based optmzaton scheme the followng test scenaro was defned. It s assumed that LNG shps arrve at the export quay every 120 hours. Shps for LPG and condensate products arrve less frequently. The dea s to evaluate the ncurred cost of one delayed LNG shp as a functon of the delay tme. Ths can be llustrated by Fg.3 where the frst LNG shp s scheduled for arrval at tme equals 48 hours and a delay s hence related to ths tme nstant. It s assumed that later LNG shps arrve on schedule. The predcton horzon was chosen to be 256 hours and the decson varables mght change every 6 hours. Fgure 3. Normal shp arrvals The producton strategy computed by the optmzer s compared wth a smple strategy where producton s reduced such that the LNG storage s full when the LNG shp arrves and hence s ready to receve LNG. Results are shown n Fg.4 where the horzontal tme axs corresponds to the tme axs n Fg.3. These results show that no extra cost for short delays up untl tme equals 88 hours. The reason for ths s that the LNG shps are scheduled to arrve when the storage
Dynamc optmzaton of the LNG value chan 7 tanks are about 74% full meanng that there s stll spare capacty. For later arrvals, however, producton must be reduced and sales ncome s lost. The optmzed producton strategy provdes a lower loss than the smple producton strategy. The reason s that producton s not only reduced, t s also redstrbuted between wells. The nne wells produce n pars of three wells from three dfferent reservors. Hence, the composton of the well streams dffer. In partcular, some wells produce more heavy components than others. Usng ths knowledge, whch s embedded n the optmzer, the optmzer redstrbutes producton such that LPG and condensate producton s reduced less than LNG producton as shown n Fg.5. Ths makes sense snce there s no delay for the LPG and condensate shps n the presented scenaro. 6. Dscusson of results Ths study shows that an approach usng smple models connected accordng to the topology of the actual producton system makes sense. An alternatve approach would have been to use the hgh fdelty smulator of the Snøhvt system. Ths has not been studed heren. Ths would, however, probably gve smlar results to the ones shown above. The results clearly show the mportance of ncludng the whole producton chan from wells to export nstead of the usual approach where the upstream part (the system from wells to the slug catcher) and the downstream part (from the slug catcher to export) are optmzed ndvdually. In the latter case the optmzer could not have antcpated the optmzed producton strategy as shown n Fg.4 and 5 snce ths requres a model of the dependences along the whole producton chan. Fgure 4. Cost ncurred by a delayed LNG shp arrval.
8 Foss and Halvorsen Fgure 5. Producton change due to delayed LNG shp arrval One reason for stressng the use of smple models s the possble use of the optmzer n a model predctve control (MPC) strategy (see e.g. Qn and Badgewell, 1996). Ths mples re-optmzng the producton strategy usng a movng predcton horzon and gves a substantal ncrease n computatonal load. MPC ntroduces feedback control whch may be mportant to account for uncertantes. An obvous uncertanty s the fact that the exact shp arrval tme s not known. The arrval tme may for nstance be defned as a stochastc varable where canddate dstrbutons mght be the ch-squared or the F-dstrbuton. In ths case t mght be necessary to formulate a stochastc optmzaton problem solvng t as a multstage stochastc program (see e.g. Frauendorfer and Haarbrucker, 2002). Ths agan ncreases computatonal load makng t even more mportant to stck wth a smple model. The predcton horzon s qute long compared to the dynamcs of the producton chan model. Hence, the dynamc ppelne and slug-catcher models were replaced by statc models. Ths reduced run tme to ¼ of ts orgnal value wthout changng results sgnfcantly mplyng that ths s a reasonable smplfcaton.
Dynamc optmzaton of the LNG value chan 9 7. Concluson The smple model of the whole producton chan combned wth model-based optmzaton offers an nterestng and feasble alternatve to optmze producton n the event of delayed shp arrval. Furthermore, the mportance of brdgng the gap between the upstream and the downstream doman by usng a model of the whole value chan s shown. References T. Backx, O. Bosgra, W. Marquardt: Integraton of model predctve control and optmzaton of processes, IFAC Symposum Advanced Control of Chemcal Processes, ADCHEM 2000, Psa, Italy, 2000. K. Dahl, Optmzaton of the LNG-value chan, Master thess, Norwegan Unversty of Scence and Technology, 2007. K. Frauendorfer, G. Haarbrucker: Stochastc and global optmzaton, Sprnger Verlag, 2002. K.T. Mdthun, Optmzaton models for lberalzed natural gas markets, PhD Thess, Norwegan Unversty of Scence and Technology, NTNU, 2007:205. J. Mula, R. Poler, J. P. García-Sabater, F. C. Laro: "Models for producton plannng under uncertanty: A revew", Internatonal Journal of Producton Economcs, 2006. J. Nocedal, S. J. Wrght: Numercal Optmzaton, Sprnger Verlag, 2000. B. Nygreen, M Chrstansen, K. Haugen, T. Bjørkvoll & Krstansen, Modelng Norwegan petroleum producton and transportaton, Annals of Operatons Research 82, 251 268, 1998. S. J. Qn, T. A. Badgewell: An overvew of ndustral model predctve control technology, CPC-V, Tahoe Cty, USA, 1996. A. Tomasgard, F. Rømo, M. Fodstad, & K. Mdthun, Optmzaton models for the natural gas value chan, n G. Hasle, K.-A. Le & E. Quak, eds, Geometrc Modellng, Numercal Smulaton, and Optmzaton: Appled Mathematcs at SINTEF, Sprnger, 2007.