A Mixed-Integer Optimization Model for Compressor Selection in Natural Gas Pipeline Network System Operations

Transcription

1 Joural of virometal Iformatics 3 () 33-4 (2004) 04JI / ISIS A Mixed-Iteger Otimizatio Model for Comressor Selectio i Natural as Pielie Network System Oeratios V. Uraikul C. W. Cha ad P. Totiwachwuthikul * Faculty of gieerig Uiversity of Regia Regia Saskatchewa S4S 0A2 Caada ABSTRACT. This aer resets a Mixed-Iteger Liear Programmig (MILP) model to otimize the comressor selectio oeratios i atural gas ielie etwork system. The objectives of atural gas ielie etwork system oeratios are to miimize the oeratio costs ad rovide sufficiet gas to the local customers. A ielie etwork system is the most cost effective way for movig fluid roducts over log distaces. I this case it is used for trasmittig atural gas from a roducer to customers. To esure demad for atural gas ca be met a disatcher turs o or off comressor(s) i order to icrease or decrease the amout of atural gas i the ielie system. Comressor selectio is oe of the most critical oeratios i the atural gas ielie etwork system because the costs associated with turig o or off the comressor make u a large ercetage of the total oeratig costs. I order to miimize the oeratig costs of the ielie system the three most crucial factors that affect the costs are itegrated ito the MILP model. The three factors iclude the caacities of comressors the eergy used to tur o the comressors ad the eergy used to tur them off. The MILP model rovides the decisio suort i determiig the otimal solutios for cotrollig the comressors. It was develoed ad verified usig the oeratio data sulied by a gas ielie comay i Saskatchewa Caada. Keywords: Comressor selectio MILP atural gas ielie otimizatio. Itroductio Sice ielie systems are the most cost effective ways for movig fluid roducts over log distaces they are imortat for trasortig gas oil etroleum roducts as well as water i Caada ad North America. ach major city i North America eeds ielie systems for its most basic eed of drikig water distributio. I additio accordig to Caadia Associatio of Petroleum Producers cubic meter of crude oil ad over 0.5 billio cubic meter of atural gas are trasorted daily i Caada over kilometers of ielie systems. Automatio of gas ielie oeratios ca otetially otimize the oeratios. The objective of the roject is to costruct a Mixed-Iteger Liear Programmig (MILP) model as art of a decisio suort system to assist oerators i the task of comressor selectio i order to satisfy customer demad with miimal oeratig cost. I atural gas ielie oeratios a disatcher is resosible for makig two vital decisios: () icrease or decrease comressio i the ielies ad (2) select idividual comressor uits to tur o/off. These decisios have a sigificat imact o effectiveess of the atural gas ielie oeratio. Whe customer demad for atural gas icreases the disatcher adds comressio to the ielie system by turig o oe or more comressors. Alteratively s/he turs off oe or more comressors to reduce comressio i the * Corresodig author: aitoo@uregia.ca ielie system if customer demad for atural gas decreases. Icorrect decisios made by the disatcher o which comressor to tur o/off icreases eergy cost or may cause customer dissatisfactio. If the ressure of the ielie dros whe customer demad icreases at least oe comressor should be oeed util the gas ressure resumes a accetable level. I additio differet comressors rovide differet comressio oututs which icreases ressure. Iaroriate oeratioal actios for startig or stoig a comressor as well as the use of differet tyes of comressors ca affect the oeratig cost. I actual oeratios a disatcher oeratig the ielie system ofte obtais iformatio o ressure ad flow from a suervisory cotrol ad data acquisitio (SCADA) system ad warig sigals from a simulatio system. For examle the simulatio system rovides iformatio o whe the system rus low o ressure which affects the disatcher s decisio o selectig oe amog may comressors to tur o or off. This may be difficult because o formal guidelies have bee established o comressor selectio i a give situatio. The decisio ca be iflueced by may factors such as oeratio costs (which cosist of fuel cost start-u cost ad maiteace cost) the ealty cost (which is icurred if the comressor does ot ru for a certai eriod of time ad avoids frequet start/sto actios) ad customer demad. Ideally the ielies should be oerated i the most cost effective maer while esurig customer demad for atural gas is met. It is imortat to reduce oeratio costs because they ormally assume more tha 60% of the total cost. To 33

2 V. Uraikul et al. / Joural of virometal Iformatics 3 () 33-4 (2004) assist the disatcher i selectig comressors a MILP model was develoed. The objectives of this study are ) to aly the MILP model to the decisio makig rocess o comressor selectio 2) to comare the solutio geerated by the MILP model with the rioritized selectio of comressors rovided by two seior oerators ad 3) to miimize the oeratio costs for the atural gas ielie etwork. The aer roceeds as follows. Sectio 2 discusses some relevat research work ad the roblem domai of atural gas ielie otimizatio. Sectio 3 discusses the methodology used to formulate the MILP model. Sectio 4 resets the alicatio of the MILP model to otimize atural gas ielie etwork oeratios ad secifically for the comressor selectio task. Sectio 5 resets some results ad discussios; ad Sectio 6 cocludes this aer. 2. Backgroud 2.. Problem Domai: Natural as Pielie Oeratios This roject was coducted i co-oeratio with a gas ielie comay i Saskatchewa Caada as a study o alyig the MILP model for comressor selectio i atural gas ielie etwork system oeratios. The focus of the roject was limited to the St. Louis ast comressor statio i the rovice of Saskatchewa Caada. A schematic of the St. Louis ast system is show i Figure. St. Louis comressor statio Melfort comressor statio lectricity comressor as comressor Niawi Hudso Bay Figure. A schematic of the St. Louis ast atural gas ielie etwork system. The system cosists of two comressor statios Melfort ad St. Louis. These comressor statios are used to suly atural gas to two customer locatios Niawi ad Hudso Bay. I St. Louis there are three comressor uits. Two of these uits are electric comressor uits ad the other is a gas comressor uit. I Melfort there are two gas comressors. A electric comressor uit rovides 250 horseower ad a gas uit rovides 600 horseower. The demad for atural gas from customers fluctuates deedig o the seaso. I the witer the demad for atural gas is usually higher tha i the summer. I additio the demad for atural gas also chages deedig o the time of day. For examle i the morig the demad is higher because the customer begis to use atural gas. I the afteroo the demad is low sice the facilities are already heated u i the morig. The customers ca also be groued ito three tyes: idustrial dehydrator ad heat sesitive customers. ach tye of customer reflects a differet atter of atural gas cosumtio as illustrated i Figure Pressure Pressure Pressure Idustrial customer Dehydrator customer Heat sesitive customer Time Time Time Figure 2. Natural gas ielie customers. The idustrial customer has the same rate of atural gas cosumtio ay time of the day. The dehydrator customer demads two set amouts of atural gas at differet eriods of time. For examle betwee 8:00 to 0:00 am the demad is m 3 /day while betwee 0:00 am to 2:00 am the demad is m 3 /day. The demad of the heat sesitive customer fluctuates over time ad is difficult to redict. I ractice the demad for atural gas ca fluctuate from m 3 /day to over m 3 /day withi oe or two hours. A demad of m 3 /day ca be hadled from St. Louis with oe comressor uit. Whe the demad goes to over m 3 /day all uits at St. Louis ad both uits at Melfort are eeded. It is the job of the oerator to kow ahead of time whe the largest volume requiremet will occur ad to be ready for it. Otherwise the system ressures at Niawi ad Hudso Bay will be below the required miimum. The grah showig suly ad demad of gas i the ielies are dislayed to the oerators. The grahs are geerated durig oeratios by a Saskergy/Trasgas (hereafter referred to as TL) simulator rogram. The dislay icludes a comressor discharge ressure curve versus custommer statio ressure curve as show i figure 3. With the grahs the disatcher or oerator is resosible for moi torig closely the volume of atural gas sulied to the St. Louis ast customers. I additio s/he eeds to decide which of the five comressors to use ad whe to tur o/off comressio i order to cotrol the volume of atural gas. Sometimes the disatchers might make uecessary start/sto decisios because they lack exeriece. A miimum of four moths is required to trai ew disatchers to oerate the system. However it takes a umber of years for them to gai roficiecy i oeratig the system smoothly ad cost effectively. 34

3 V. Uraikul et al. / Joural of virometal Iformatics 3 () 33-4 (2004) Pressure (ka) 3000 Comressor Discharge Pressure (suly) Customer d-oit Delivery 2500 Pressure (demad) Figure 3. Time (hr) Demad versus suly grah. The tyical dislay show i Figure 3 rovides ressure iformatio to disatchers. The two curves idicate the relatioshi betwee demad ad suly ad the ga betwee the two curves is called the comfort zoe (CZ). If the ga betwee these curves is wide the customer satisfactio is guarateed but the cost is high. If the comfort zoe is too arrow the the oeratio is cost effective but future customer demad may ot be satisfied. Hece the disatcher eeds to select a comressor to icrease ressure i the ielies while maitaiig the otimum oeratig ressure i the ielie system Requiremets for the Methodology There are a umber of requiremets for the methodology for otimizatio of the atural gas ielie oeratios. Firstly the methodology eeds to be robust so as to take ito cosideratio most imortat asects of comressor selectio for atural gas ielie oeratios ad secodly it should rovide satisfactory results. The Mixed-Iteger Liear Programmig (MILP) model is believed to meet these requiremets due to the followig cosideratios. Firstly the MILP model costrais the decisio variables to assume oly iteger values (i.e. or 0) i the otimal solutio. The use of iteger variables ca otimize the roblem where the solutio ca either be 0 or. For examle a decisio variable x called a 0- iteger variable ca be used for modelig the o/off decisio of whether to tur o or off a comressor. Secodly the MILP model ca also be used to otimize oeratig costs. I the domai of gas comressor selectio comressors ca be tured either o or off. Thus a comressor oeratio ca be rereseted as 0 or. Also comressor selectio requires a tye of iteger rogrammig i which ot all the variables to be otimized have iteger values. Hece it is more aroriate to use Mixed-Iteger Liear Programmig for modelig comressor oeratios of atural gas ielie etwork systems. Due to the liear ature of the oeratio costs it ca be exressed mathematically i the objective fuctio of the MILP model but the results must comly with defied costraits such as the demad for atural gas withi a secified time horizo Relevat Literature Several researchers used Mixed-Iteger Liear Programmig (MILP) i solvig roblems i idustry. Vasquez- Alvarez ad Pito [2003] develoed a MILP model for the sythesis of rotei urificatio rocesses by icororatig losses i the target rotei alog with the urificatio rocess. The model rovides some guidelies for evaluatig the trade-off betwee roducts by urity ad quatity. Xie et al. [2003] alied a MILP model to maage comilig time for dyamic voltage scalig (DVS) settigs. The model was formulated to accout for DVS eergy switchig overhead by rovidig cotrol o settig ad by cosiderig multile data categories i the otimizatio. Jai ad rossma [200] combied the MILP aroach with a costrait rogrammig (CP) techique to solve roblems of job schedulig o arallel machies. Adjima et al. [998] formulated a mixediteger otimizatio model to solve roblems i the rocess of flowsheets that covert raw materials ito desired roducts. Maulik et al. [992] reseted a ew cell-level aalog circuit sythesis methodology by alyig mixed-iteger oliear rogrammig. Abil et al. [993] suggested that the Mixed- Iteger Liear Programmig MILP techique had saved $20 millio er year over the eriod of ad $3-5 millio from at America Airlies. Ciriai [998] suggested that the MILP techique could be used as a rerocessor while combiatorial roblems with a flat objective fuctio ca beefit from the use of heuristics. He also cocluded that model formulatio could rovide a better iteger aroximatio. Dilleberger ad Wollesak [993] reorted o the successful itegratio of the MILP techique i the decisio suort system of IBM's Sidelfige lat. Ballitji [993] described the MILP techique that was used to cotrol mode switchig at accetable levels. 3. Methodology I this aer the methodology of a MILP model has bee tailored to otimize atural gas ielie etwork oeratios articularly i the comressor selectio task. For this task the model s mai fuctios cosist of decisio variables a objective fuctio ad costrait equatios. The decisio variables determie the results of the objective fuctio ad costraits. The objective fuctio reresets the total oeratig costs withi a secified time horizo. I this study the oeratig cost is the sum of the fuel costs maiteace cost for each comressor the start-u cost whe a comressor is started after beig shut dow ad ealty cost for ot oeratig a comressor cotiuously for a certai eriod of time. The followig sectio will describe the MILP model formulatio. 35

4 V. Uraikul et al. / Joural of virometal Iformatics 3 () 33-4 (2004) 3.. MILP Model Formulatio 3.. Decisio Variables The decisio variables determie the status of comressors ad rereset the model s advice o how to oerate the comressors i the atural gas ielie system. I atural gas ielie oeratios the status of a comressor ca either be o or off. I the St. Louis ast system there are two kids of comressor: gas or electric. The decisio variables for this model are defied as i which reresets the status of gas comressor i i eriod while i deotes the status of electric comressor i i eriod. The values of i ad i ca be defied as follows: i if the comressor i is tured o i eriod = i 0 if the comressor i is tured off i eriod where i = if the atural gas comressor i is selected to oerate i eriod ad 0 otherwise; i = if the electric comressor i is selected to oerate i eriod ad 0 otherwise. The decisio variables are used for determiig the oeratig costs. The objective fuctio of the MILP model ca be formulated by icororatig the decisio variables Objective Fuctios The objective fuctio is formulated for determiig the otimal oeratig costs associated with comressor oeratios withi a secified umber of oeratig eriods. I this case study the MILP model is formulated to determie the otimal sets of selected comressors amog may ossible selected combiatios of comressors ad to miimize the total oeratig costs withi six oeratig eriods. The reaso for usig six oeratig eriods as the time horizo is that a disatcher ca have eough time to effectively cotrol the volume of atural gas i the ielie system if the selected comressors are give withi six eriods. The total oeratig cost is the sum of fuel cost maiteace cost start-u cost ad shutdow cost. The formulae to calculate these costs must be develoed before the objective fuctio ca be fialized. The equatios for calculatig the fuel cost maiteace cost start u cost ad shutdow cost are described i the followig. Fuel cost Fuel cost is the cost associated with the amout of eergy used i oeratig each comressor withi a time horizo. I geeral comressors have differet rates of eergy cosumtio. For examle a electric comressor utilizes more eergy i turig o/off tha a gas comressor. As a result the fuel cost for oeratig electric comressor is ormally higher tha that of a gas comressor. The fuel cost of electric ad gas comressor ca be calculated with the followig equatios. Mi Fgi i () i= = Mi Fei i (2) i= = where Fg is the fuel cost of gas comressor i is gas comressor i i eriod Fe is the fuel cost of electric comressor i is electric comressor i i eriod. Maiteace cost The maiteace cost refers to regular maiteace cost of each comressor. ach comressor ca oly be oerated for a limited umber of hours after which it must be shut off for maiteace. For examle i St. Louis ast atural gas ielie system the total oeratig hours for each comressor may ot exceed 000 hours. After 000 hours a comressor should be serviced ad maitaied. The followig equatio is used for calculatig the maiteace cost for gas ad electric comressor resectively. Mg i (3) i= = Me i (4) i= = where Mg ad Me are the maiteace costs of gas comressor ad a electric comressor resectively i is the gas comressor uit i i eriod ad i is electric comressor i i eriod. Start-u cost Whe a comressor is tured o there is a cost attached due to the eergy set durig its oe oeratios. The start-u cost ca be calculated usig the followig equatios: Sg i Sg i i (5) i= = Se i Se i i (6) i= = where Sg is the start u cost of a gas comressor Se is the start u cost of a electric comressor i is the gas comressor uit i i eriod ad i is the electric comressor uit i i eriod Shutdow cost Shutdow cost is the cost icororated i the MILP model to avoid comoet wear of each comressor. ach comressor should be selected so that the umber of times of turig o/off is miimized to reduce comoet wear. After a comressor is tured o it should be cotiuously oeratig for as log as ossible which is assumed to be a miimum of 36

5 V. Uraikul et al. / Joural of virometal Iformatics 3 () 33-4 (2004) 3 hours i this examle situatio. Whe a comressor is shut off because it is ot eeded it should be off for as log as ossible. The start u or shut off cost of a comressor is give as a ealty cost ad this cost is added to the total oeratio costs. For examle comressor ad comressor 2 rovide the same amout of horseower. I time iterval comressor is selected to tur o to meet the customer demad while comressor 2 is ot eeded. I time iterval 2 the customer demad remais the same. Therefore comressor remais o ad comressor 2 remais off i order to reduce total oeratig cost. Based o the exertise rovided by two seior oerators from a gas trasortatio comay each comressor should cotiuously oerate for at least 3 hours to avoid comoet wear. The followig equatio is used to calculate the ealty cost of the comressor ruig for less tha 3 hours. 3 (3 i i2 i3 ) + (3 i2 i3 i4) + PCg + (3 i3 i4 i5 ) + (3 i4 i5 i6 ) i= 2 (3 i i2 i3 ) + (3 i2 i3 i4) + PCe + (3 i3 i4 i5 ) + (3 i4 i5 i6 ) i= where PCg is the ealty cost if a gas comressor is ruig for less tha 3 eriods PCe is the ealty cost if a electric comressor is ruig for less tha 3 eriods i is gas comressor i i eriod i is electric comressor i i eriod. After the equatios () to (7) for calculatig the fuel cost maiteace cost start-u ad shutdow cost have bee formulated the objective fuctio ca be fialized as follows. mi Z = ( Fg + Mg + Sg) Sg i i i i= = i= = i ( Fe Me Se) Se i i i= = i= = (3 i i2 i3 ) + (3 i2 i3 i4) + PCg + (3 i3 i4 i5 ) + (3 i4 i5 i6 ) i= (3 i i2 i3 ) + (3 i2 i3 i4) + PCe + (3 i3 i4 i5 ) + (3 i4 i5 i6 ) i= 3..3 Costraits The objective fuctio as fialized i equatio (8) is subjected to the followig costraits: Customer demad The rimary objective of atural gas ielie etwork oeratios is to deliver atural gas to customers accordig to their demad. Durig oeratios the disatcher turs o or off comressors i order to icrease ressure i the ielies (7) (8) so that atural gas ca be trasorted from the comressor statios to the customer locatios. Break horseower (BHP) defies the caacity of a comressor which icreases ressure i the ielie system. Accordig to the seior oerators from the St. Louis ast atural gas ielie system BHP requiremet ca be calculated usig equatio (9) (Uraikul et al 2000) or ca be obtaied from the horseower requiremet chart show i Figure 4. BHP requiremet = (St. Louis flow + Melfort flow) 32 From equatio (9) the disatcher ca obtai the horse ower requiremet usig St. Louis ad Melfort flows. For examle i Figure 4 if the flows are lower tha /day o additioal horseower is required. Total St. Louis ast BHP Requiremet Total St. Louis ast BHP Requiremet BHP = 2774 (St. Louis flow + Melfort flow) - 32 BHP=274 x St. Louis ast Volume 0^3/day (load) Figure 4. St. Louis ast Volume 0 3 /day (load) Horseower requiremet chart. where BHP is the break horseower requiremet S_Flow is the gas flow measured at St. Louis statio ad M_Flow is the gas flow measured at Melfort statio. The customer-demad costrait ca be rereseted usig the followig equatio. ( ) + He ( ) D (0) i i i i i= = i= = where i is the horse ower of a gas comressor i ad He i is the horse ower of a electric comressor i D is the customer demad i eriod i is gas comressor i i eriod i is electric comressor i i eriod. Status of comressors The status of a comressor ca either be o or off thus the value of i ad i is limited to 0 or ( if the comressor is o ad 0 otherwise). The followig equatios are formulated i order to limit the value of i ad i to be the desired value of 0 or. (9) 37

6 V. Uraikul et al. / Joural of virometal Iformatics 3 () 33-4 (2004) i + i i i 0 i () i + i i i i (2) i (3) i i i i i + i i i 0 i (4) i + i i i i (5) i (6) i i i i 4. Alicatio of the MILP Model to a Natural as Pielie Network System Havig comleted the requiremets for settig u the MILP model the model ca the be alied to a actual atural gas ielie etwork system. I geeral each atural gas ielie system adots differet rules for utilizig the comressors. The assumtios for the St. Louis ast system are exlicated as follows. ) ach comressor must be take ito service after it has bee oeratig for 000 hours. Therefore the maiteace cost for each comressor is equal to /000 times the maiteace cost of each comressor. 2) Customer demad must be satisfied i every eriod ad the amout of the demad is coverted from the load of St. Louis ad Melfort flow to BHP requiremet based o the BHP requiremet chart. 3) A comressor usually requires to 2 days service. This is ot modeled sice our time horizo is oly 6 hours ad at the begiig of each hour it is reasoable to assume that the availability of each comressor would be kow with certaity. 4) A comressor should be oeratig for as log as 3 hours to avoid comoet wear otherwise ealty cost will be alied. 5) The customer demad must be kow with certaity for 6-hour eriods. 6) The locatio of comressors does ot affect the trasmissio efficiecy of gas from the St. Louis ad Melfort statios to Niawi or Hudso Bay. Based o these assumtios the MILP model was alied to the gas ielie system i the St. Louis ast system. There are two comressor statios i this sectio of the ielie system: the St. Louis ad Melfort statios. There are two electric comressors labeled ad 2 ad oe gas comressor labeled at the St. Louis statio while the Melfort statio has two gas comressors labeled 2 ad 3. These com- ressors ca rovide differet caacities of BHP (break horseower) so as to adjust the gas ressure i the ielie for differet situatios. The atural gas is trasmitted from the two comressor statios to the two customer locatios of Niawi ad Hudso Bay. The imortat arameters associated with each comressor are listed as follows: = electric comressor uit (BHP = 250 km 3 /d) 2 = electric comressor uit 2 (BHP = 250 km 3 /d) = gas comressor uit (BHP = 600 km 3 /d) 2 = gas comressor uit 2 (BHP = 600 km 3 /d) 3 = gas comressor uit 3 (BHP = 600 km 3 /d) Based o the objective fuctio (8) the objective fuctio of the St. Louis ast system ad its corresodig costraits ca be fialized as show i Table. The model otimizes the atural gas ielie oeratios by rovidig the otimal results of comressor selectio based o the required arameters secified i the model. These arameters iclude the tyes of comressors the umber of comressors i the ielie system ad the umber of eriods to be otimized. Havig idetified the imortat arameters the oeratig costs that iclude the fuel cost of each comressor maiteace cost start u cost ad shutdow cost ca be substituted ito the model. However these costs caot be fixed because they vary deedig o the oeratig seasos ad ricig of gas. The oeratig costs ad results geerated by the MILP model will be discussed i followig sectio uder Results ad Discussios. 5. Results ad Discussios This sectio describes the results geerated by the MILP model ad comares the results with the rioritized orders for ruig comressors rovided by two seior oerators from the St. Louis ast atural gas ielie system. Before the model ca be iitialized the followig iuts must be idetified: Horse ower of each comressor is kow with certaity as metioed i sectio 4. I the St. Louis ast system the BHP of each comressor is listed as follows: Horse ower of gas uit () = 600 gas uit 2 (2) = 600 gas uit 3 (3) = 600 electric uit (He) = 250 electric uit 2 (He2) = 250 The iitial values of comressor status must be rovided to the model because the availability of each comressor must be kow with certaity before the calculatio is iitialized. For this sceario the iitial value of each comressor is assumed as 0 meaig that all uits are off i the begiig. The iitial value of gas comressor uit (0) = 0 gas comressor uit 2 (20) = 0 gas comressor uit 3 (30) = 0 electric comressor uit (0) = 0 electric comressor uit 2 (20) = 0 Oeratig costs are ot kow with certaity ad always varied deedig o the oeratig seaso ad gas ricig. For this sceario the fuel cost maiteace cost start-u 38

7 V. Uraikul et al. / Joural of virometal Iformatics 3 () 33-4 (2004) Table. Objective Fuctio ad Costraits of the St. Louis ast System Mi: (Fg + Mg + Sg) + (Fg + Mg + Sg) 2 + (Fg + Mg + Sg) 3 + (Fg + Mg + Sg) 4 + (Fg + Mg + Sg) 5 + (Fg + Mg + Sg) 6 + (Fg + Mg + Sg) 2 + (Fg + Mg + Sg) 22 + (Fg + Mg + Sg) 23 + (Fg + Mg + Sg) 24 + (Fg + Mg + Sg) 25 + (Fg + Mg + Sg) 26 + (Fg + Mg + Sg) 3 + (Fg + Mg + Sg) 32 + (Fg + Mg + Sg) 33 + (Fg + Mg + Sg) 34 + (Fg + Mg + Sg) 35 + (Fg + Mg + Sg) 36-(Sg) 0-(Sg) 2 - (Sg) 32-(Sg) 43-(Sg) 54-(Sg) 65-(Sg) 220-(Sg) (Sg) 2322-(Sg) (Sg) 2524-(Sg) 2625-(Sg) 330-(Sg) (Sg) 3332-(Sg) 3433-(Sg) 3534-(Sg) (Fe + Me + Se) + (Fe + Me + Se) 2 + (Fe + Me + Se) 3 + (Fe + Me + Se) 4 + (Fe + Me + Se) 5 + (Fe + Me + Se) 6 + (Fe + Me + Se) 2 + (Fe + Me + Se) 22 + (Fe + Me + Se) 23 + (Fe + Me + Se) 24 + (Fe + Me + Se) 25 + (Fe + Me + Se) 26-(Se) 0-(Se) 2 -(Se) 3 2-(Se) (Se) 5 4-(Se) 6 5-(Se) 2 20-(Se) 22 2-(Se) (Se) (Se) (Se) PCg (3--2-3) + PCg ( ) + PCg (3--2-3) + PCg ( ) + PCg ( ) + PCg ( ) + PCg ( ) + PCg ( ) + PCg ( ) + PCg ( ) + PCg ( ) + PCg ( ) + PCg ( ) + PCg ( ) + PCe (3--2-3) + PCe ( ) + PCe ( ) + PCe ( ) + PCe ( ) + PCe ( ) + PCe ( ) + PCe ( ) Subject to: )+ 2 2)+ 3 3) +He )+He 2 2) >= D ; 2)+ 2 22)+ 3 32)+He 2)+He 2 22) >= D 2; 3)+ 2 23)+ 3 33)+He 3)+He 2 23) >= D 3; 4)+ 2 24)+ 3 34)+He 4)+He 2 ( 24) >= D 4; 5)+ 2 25)+ 3 35)+He 5)+He 2 25) >= D 5; )+ )+ )+He )+He ) >= D ; ( 0) >= 0; ( 0) <= ; ) <= 0; 2+ - (2 ) >= 0; 2+ - (2 ) <= ; ) <= 0; (3 2) >= 0; 3+2 -(3 2) <= ; ) <= 0; (4 3) >= 0; (4 3) <= ; ) <= 0; (5 4) >= 0; (5 4) <= ; ) <= 0; (6 5) >= 0; (6 5) <= ; ) <= 0; ( 2 20) >= 0; (2 20) <= ; ) <= 0; ( 22 2) >= 0; ( 22 2) <= ; ) <= 0; ( 23 22) >= 0; (23 22) <= ; ) <= 0; (24 23) >= 0; (24 23) <= ; ) <= 0; ( 25 24) >= 0; (25 24) <= ; ) <= 0; ( 26 25) >= 0; (26 25) <= ; ) <= 0; (3 30 ) >= 0; (3 30) <= ; ) <= 0; (32 3) >= 0; (32 3) <= ; ) <= 0; (33 32) >= 0; (33 32 ) <= ; ) <= 0; (34 33) >= 0; (34 33) <= ; ) <= 0; (35 34) >= 0; (35 34) <= ; ) <= 0; (36 35) >= 0; (36 35) <= ; ) <= 0; ( 0) >= 0; ( 0) <= ; ) <= 0; 2+ - (2 ) >= 0; 2+ - (2 ) <= ; ) <= 0; (3 2) >= 0; (3 2) <= ; ) <= 0; (4 3) >= 0; (4 3) <= ; ) <= 0; ( 5 4) >= 0; (5 4) <= ; ) < = 0; (6 5) >= 0; (6 5) <= ; ) <= 0; (2 20) >= 0; (2 20) <= ; ) <= 0; (22 2) >= 0; (22 2) <= ; ) <= 0; (23 22) >= 0; (23 22) <= ; ) <= 0; (24 23) >= 0; (24 23) <= ; ) <= 0; (25 24) >= 0; (25 24) <= ; ) <= 0; (26 25) >= 0; (26 25) <= ; ) <= 0; 39

8 V. Uraikul et al. / Joural of virometal Iformatics 3 () 33-4 (2004) cost ad shutdow cost are assumed as follows. Fuel cost of gas comressor (Fg) = 50 Maiteace cost of gas comressor (Mg) = 3 Start-u cost of gas comressor (Sg) = 40 Fuel cost of electric comressor (Fe) = 35 Maiteace cost of electric comressor (Me) =.5 Start-u cost of electric comressor (Se) = 30 Pealty cost of gas comressor (PCg) = 33 Pealty cost of electric comressor (PCe) = 23. The customer demad must be give i 6 oeratig eriods. I the real oeratio the demad ca be obtaied usig the comay s forecastig facility. For this sceario the customer demad i 6 eriods is assumed as follows: Customer demad i eriod (D) = 200 eriod 2 (D2) = 700 eriod 3 (D3) = 850 eriod 4 (D4) = 350 eriod 5 (D5) = 280 eriod 6 (D6) = 800 Havig idetified the required iuts which iclude BHP of each comressor oeratig costs iitial status of comressor ad customer demad the model geerated results as follows: Period. 2 Period Period Period Period Period Total oeratio costs is $ The MILP model geerated the recommedatios o comressor selectio oeratios i 6 eriods with the total oeratig costs of $47. To ivestigate the otimal solutio based o the arameters rovided the results geerated by the model will be comared to the rioritized orders of ruig comressors rovided by two seior oerators from the St. Louis ast System. The two exert oerators idicated that i real oeratios there must be oe comressor uit which always oerates to maitai the miimum ressure i the ielie. For the St. Louis ast system the disatcher will radomly select oe comressor amog the five comressors to oerate all the time deedig o the availability of the comressor ad the umber of hours before the comressor is take off for maiteace. For this sceario a electric comressor at the St.Louis comressor statio () will be selected as the all-time-ruig uit. For a give amout of horseower required a differet combiatio of comressor uits ca be tured o/off based o the seior oerators kowledge o the rioritized order of ruig comressors which is listed as follows.. Free flow (o comressio) always o 2. (0 < BHP < 800): tur o St. Louis gas comressor 3. (800 BHP < 200): tur o St. Louis gas comressor ad Melfort gas comressor 2 4. (200 BHP < 600): tur o St. Louis gas comressor ad Melfort gas comressor 2 ad St. Louis electric comressor 2 5. (600 BHP < 2200): tur o St. Louis gas comressor ad electric comressor 2 ad Melfort gas comressor 2 ad gas comressor 3. With the same set of data o customer demad i 6 oeratig eriods as reviously rovided to the MILP model the followig combiatios are the results obtaied from the rioritized orders of ruig comressors: Period : + Period 2: + Period 3: Period 4: Period 4: Period 5: The total oeratio costs based o these combiatios is $69. I comariso to the results geerated by the MILP model the comay ca otetially save $29.5 or 3% (29.6/69) of the oeratig costs based o this sceario. The model has also bee alied uder various scearios of oeratig costs ad customer demads. It ca be observed from the results that the fuel cost er BHP uit has a major imact o the model. For examle if the fuel cost er uit of electric comressor is 50% higher tha that of the atural gas comressor the MILP model would suggest to oly oerate gas comressors while lettig electric comressors stay off. I real oeratios however the cost of oeratig the electric comressor is relatively higher tha that of the gas comressor but ot too high. I short if the ratio of fuel cost er uit of electric comressor ad gas comressor is ot high the model would rovide soud advice o the comressor selectio to the disatcher. 6. Coclusios I atural gas ielie etwork system oeratios comressor selectio is oe of the most critical decisios because satisfactio of customer demad for atural gas directly deeds o turig o or off the comressors. If the disatcher fails to otimally oerate the comressors due to a lack of iformatio the comay will suffer losses. A Mixed- Iteger Liear Programmig (MILP) model ca rovide suort to this crucial decisio makig rocess by suggestig the solutio that miimizes oeratig costs. The four major costs associated with the task of comressor selectio are cosidered i the objective fuctio. These costs iclude fuel cost maiteace cost start-u cost ad shut dow cost. The objective of the MILP model is to reduce these costs while esurig customer demads are satisfied. A umber of advatages of usig the MILP model to hel solve the comressor selectio roblem are observed as follows: The model ca hel the disatcher i decidig which 40

9 V. Uraikul et al. / Joural of virometal Iformatics 3 () 33-4 (2004) amog the five comressors to tur o or off based o the otimal oeratig costs. I cotrast to the rioritized order of ruig comressors which ca oly be used i a hourly basis the model was exteded to cosider six oeratig eriods ad covered a loger duratio. The develoed MILP model ca be exteded to cover other areas of the atural gas ielie system i Saskatchewa such as that of the city of Regia Saskatchewa. Users ca easily make chages or modify the arameters i the model. Hece the model ca be adated for variatios i seaso ad gas rices which are imortat determiats for the oeratig costs of the comressors. Some weakesses i the MILP aroach are oted as follows: Sice the customer demad withi six oeratig eriods must be kow before the MILP model ca be alied accuracy of the redicted customer demad is imortat. If the customer demad is ot accurately redicted the model s recommedatios o comressor selectios may ot be accurate. The model igored the cosideratio of the hysical distaces betwee the comressor statios ad the customer locatios. Hece the results rovided by the MILP model may ot be accurate because a comressor located ear the customer locatios may suly atural gas to the customers faster tha a comressor located farther away from the customers. Ackowledgmets. We are grateful for the co-oeratio ad suort of Saskergy/Trasgas i this roject. We also would like to ackowledge the geerous fiacial suort of a Strategic rat from Natural Scieces ad gieerig Research Coucil (NSRC) of Caada. Refereces Adjima C.S. Schweiger C.A. ad Floudas C.A. (998). Mixed-Iteger Noliear Otimizatio i Process Sythesis i D.Z. Du ad P.M. Pardalos (ds.) Hadbook of Combiatorial Otimizatio Kluwer Academic Publishers Bosto Dordrecht. Abil R. elma. Patty B. ad Taga R. (99). Recet advaces i crew-airig otimizatio at America airlies. Iterfaces Balas. Ceria S. ad Coruejols. (998). A lift-ad-roject cuttig lae algorithm for mixed 0- rograms. Math. Program Ballitij K. (993). Otimizatio i refiery schedulig: modelig ad solutio Otimizatio i Idustry Mathematical Programmig ad Modelig Techiques i Practice Joh Wiley & Sos Ciriai T. (998). Model structures ad otimizatio strategies. Otimiz. Id. J. Mauf. Sci. g Dilleberger C. ad Wollesak A. (993). Demad allocatio for caacity otimizatio: a solutio i IBM maufacturig. Otimiz. Id. Comut. Math. Al. 37(5) Jai V. ad rossma I.. (200). Algorithms for hybrid MILP/CP models for a class of otimizatio roblems. INFORMS J. Comut. 3(4). Kritihat W. Totiwachwuthikul P. ad Cha C.W. (998). Pielie etwork modelig ad simulatio for itelliget moitorig ad cotrol: a case study of a muicial water suly system. Id. g. Chem. Res. J Maulik P.C. Carley L.R. ad Rutebar R.A. (992). A mixed-iteger oliear rogrammig aroach to aalog circuit sythesis i Aual ACM Desig Automatio Coferece Proc. of the 29 th ACM/I Coferece o Desig Automatio Coferece Aaheim Califoria USA Radall D. Clelad L. Kuehe S.C. ad Sheer.W. (997). Water suly laig simulatio model usig mixed-iteger liear rogrammig gie. The ASC J. Water Resour. Pla. Maage. 23(2) Uraikul V. Cha W.C. ad Totiwachwuthikul P. (2000). Develomet of a exert system for otimizig atural gas ielie oeratios. xert Syst. Al. J. 8(4) Vasquez-Alvarez. ad Pito J.M. (2003). A mixed iteger liear rogrammig model for the otimal sythesis of rotei urificatio rocesses with roduct loss. Chem. Biochem. g. Q. 7() Xie F. Martoosi M. ad Malik S. (2003) Comile-time dyamic voltage scalig settigs: Oortuities ad limits PLDI 03 Sa Diego Califoria USA. 4