Mooring Cost Sensitivity Study Based on Cost-Optimum Mooring Design

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1 Proceedngs of Conference 8 Korean Socety of Ocean Engneers May 9-3, Cheju, Korea Moorng Cost Senstvty Study Based on Cost-Optmum Moorng Desgn SAM SANGSOO RYU, CASPAR HEYL AND ARUN DUGGAL Research & Development, SOFEC, Inc., Houston, Texas, U.S.A. KEY WORDS: Offshore moorng desgn, FPSO turret moorng, Harmony Search, Optmzaton ABSTRACT: The paper descrbes results of a senstvty study on an optmum moorng cost as a functon of safety factor and requred maxmum offset of the offshore floatng structure by fndng the anchor leg component sze and the declnaton angle. A Harmony Search (HS) based moorng optmzaton program has been appled to conduct ths study. Ths moorng optmzaton model was ntegrated wth a frequency-doman global moton analyss program to assess both cost and desgn constrants of the moorng system. To fnd a trend of anchor leg system cost for the proposed senstvty study, optmum costs after a certan number of teraton were found frst and they were compared. For a case study a turret-moored FPSO wth 3 X 3 anchor leg system was consdered. To better gude search for the optmum cost, three dfferent penalty functons were appled. The results show that the presented HS-based cost-optmum offshore moorng desgn tool can be used to fnd optmum moorng desgn values such as declnaton angle and horzontal end pont separaton as well as cost-optmum moorng system n case ether the requred maxmum offset or factor of safety vares. 1. Introducton As other engneerng desgn cycles the offshore moorng desgn requres sgnfcant amount of desgn cycles wth the satsfacton of the complex desgn constrants n order to acheve an ecomcally compettve soluton (Ryu et al., 7). Ryu et al. (7) presented anchor leg cost optmzaton va harmony search and concluded that the harmony search was able to fnd cost optmum solutons. Fyllng (1997) and Fyllng and Kleven () address an applcaton of moorng optmzaton of deepwater moorng and rser rsers. A sngle pont moorng of an FPSO was selected for a case study. Ths study focuses on moorng cost senstvty of the anchor leg system optmzed by usng harmony search (HS) algorthm. Parameters that change for ths senstvty study nclude safety factor and requred maxmum offset of the floatng platform. Ths paper addresses HS-based moorng optmzaton determnng length and dameter of each moorng component, declnaton and horzontal end pont separaton dstance that satsfes requred safety factor of the moorng lne top tenson, maxmum platform offset, and bottom chan length. In ths paper the HS algorthm s summarzed frst. Secondly, appled penalty functons are presented. Lastly, moorng cost senstvty results for a deepwater FPSO moored by 3 x 3 anchor leg system are summarzed.. Harmony search algorthm Compared to other smulaton-based meta-heurstc optmzaton algorthms such as smulated annealng, tabu search, and generc algorthm (Smpson et al., 1994; Cunha and Sousa, 1999), HS was adopted from muscal process of fndng 'pleasant harmones.' For nstance, when several tes from dfferent muscal nstruments are played smultaneously on a random bass and ths process s repeated, there s a possblty to fnd better harmones. In HS, these better harmones are saved n a certan sze of memory by replacng the worst harmony n the memory untl the pre-defned maxmum number of mprovsaton, generatng a new harmony, s reached. HS has relatvely smple structure and does t requre complex mathematcal gradents for the functons n optmzaton process. Thus, t s free from mathematcal dvergence n the mddle of computaton (Geem, 6b). HS also does t requre startng values for desgn varables. Thus, t has better chance to fnd global optmum rather than to be entrapped n local optma (Geem et al., 1). By nature, HS can effcently handle dscrete varables as well as contnuous varables (Lee and Geem, 5). However, conventonal gradent methods handle contnuous varable only, whch causes a problem when desgn varables have dscrete values, such as commercal szes made n a factory. Page 1 of 5

2 Proceedngs of Conference 8 Korean Socety of Ocean Engneers May 9-3, Cheju, Korea To round contnuous values up to dscrete values may cause the fnal desgn worse (Geem, 6a). When compared wth genetc algorthm (GA) as ather popular soft-computng method, HS overcame the drawback of GA's major mechansm by explctly consderng the relatonshp among desgn varables (Geem, 6c). Step 1: Parameter Set-up HMS HMCR PAR No. of Improvsaton (Iter) Step : HM Intalzaton Soluton vector generated Step 4: HM Update If (new cost) < (worst cost n HM) Then replace the worst harmony wth the new harmony 1. Global Moton Analyss. Cost & Penalty Calc Step 5: Repeat or? If ( < Iter) Then Go To Step 3 Elsef (I = Iter) End Step 3: Improvse New Harmony Select a new soluton vector or Generate t Note: dotted lne represents loop Fg. 1 Flow chart of HS algorthm for desgnng a cost-optmal moorng system (Ryu et al., 7). Fundamental fve steps of a HS for the cost-optmum moorng system desgn are shown n Fg. 1, and they are detaled n Ryu et al. (7). A typcal moorng desgn cycle s summarzed n Fg.. In ths present study moorng desgn for only ntact case was consdered. 3. Penalty Functons Implemented three desgn constrants nclude (1) factor of safety (FS) for the top tenson of the ntact case, () uplft of the bottom chan, and (3) requred maxmum platform offset. To better gude search for a cost optmum soluton, followng three dfferent types of penalty functons were employed for the above mentoned three desgn constrants, respectvely: p1 = c ( Tmax / MBL) (1) p = caverage () p3 = c ( dmax / dmax, desgn) (3) where p ( = 1,,3) represents cost penalty, c calculated materal cost, c average average cost of the saved harmony memory, T calculated maxmum top tenson, MBL mnmum max break load, d max calculated maxmum offset, and d max,desgn requred maxmum desgn offset. 4. Case Study: FPSO Moorng Desgn As a case study an FPSO turret-moored by 3 x 3 chan-wre-chan anchor leg system s consdered. The FPSO wth a permanent turret moorng system n water depth (WD) of 8m was defned as the base case. The FPSO vessel partculars used are detaled n Ryu et al. (7). Followed s the summary of the desgn constrants for the base case: maxmum FPSO offset = 7.5% of water depth; FS for ntact case top tenson = 1.67 (mnmum break load MBL); and uplft at the anchor poston. Each anchor leg s made up of a combnaton of studless chan and spral strand wre rope. The objectve functon (.e. total cost of moorng system) s also smplfed as: N C = f( L, d ) (4) = 1 where f ( L, d ) s the cost of moorng component wth length L and d dameter, and N s the number of moorng components n the moorng system. The sgn conventons utlzed for the analyss of motons and loads n earth-fxed and vessel-fxed local coordnate systems are summarzed n Ryu et al. (7). The nne anchor legs for the FPSO vessel are arranged n three groups of 3 anchor legs each. One group of anchor legs s orented 15 degrees CCW from North; the other two groups are arranged 1 degrees apart from the Northern group. The anchor leg farleads are separated by 13 degrees n each group on the turret, and arranged on an 8-meter radus. The anchor legs depart the turret at 5-degree spacng between adjacent legs n a group. The anchor radus s varable to be determned as a result of the optmzaton process. The ballast load draft (8.55m) was appled. 4.1 Desgn envronmental condton The desgn envronmental condton s summarzed n Table 1. A JONSWAP spectrum was used to model both the wnd waves and the swell, whle the NPD spectrum was used to model the gustness of the wnd. Page of 5

3 Proceedngs of Conference 8 Korean Socety of Ocean Engneers May 9-3, Cheju, Korea Modelng of Envronmental Forces Hydrodynamc Calculatons 3 4 EA = (11.86 d -.4 d ) 1 /981 (5) W = A d Szng of Moorng Lnes Global Analyss - Intact Case Tenson & Offset FS acceptable? Max Offset satsfed? Global Analyss - Damaged Case Tenson & Offset FS acceptable? Max Offset satsfed? Fatgue Analyss Desgn lfe satsfed? where A for wet weght s.17 and.195 for dry weght. The cost estmate of the studless chan and wre s based on the followng equatons: (6) C chan =.63 d l C wre =.3415 d l (7) where C s cost n USD ($), d the dameter n mm, and l the length n meter. 4.3 Harmony search computaton A total of 1, teratons were performed for each case to fnd cost-optmal moorng desgns, and Fg. 3 shows the trend of average total anchor leg system cost n harmony memory. The horzontal end pont separaton between farlead and anchor s shown n Fg. 4. Fgure 5 presents a hstogram of the top chan declnaton angle dstrbuton after 1, teratons. Note: Dotted lne (red) represents moorng desgn cycle Fg. Flowchart of typcal moorng desgn cycle Table 1 Summary of desgn envronmental condton. Value Headng [deg] Wnd 39 kts 185 Current 1 kts 185 Wave Hs = 19 m 15 Tp = 137 s γ = 1 Swell Hs = 1 m Tp = 13 s γ = Estmate of moorng lne propertes and cost Table Coeffcents for estmaton of wre rope propertes. Unt A B MBL MT Axal Stffness MN Wet Weght kg/m Dry Weght kg/m Table 3 Input bound for farlead declnaton angle. Lower (deg) Upper (deg) Declnaton 7 In ths case study, the appled values of the HS parameters are: HMS = 1 HMCR =.95 PAR =.8 and NI = 1,. The nput lower and upper bounds for each desgn parameter,.e. declnaton angle, lengths and dameters of top chan, wre, and bottom chan are summarzed n Table 3. Expressons for moorng lne propertes such as mnmum break load (MBL), axal stffness and weght were derved usng catalogue data suppled by manufacturers. For wre rope the propertes can be descrbed as a functon of dameter d usng the B formula: y = A d, where d s the dameter of the lne n mllmeters, and A and B are constant. Table provdes the coeffcents for the varous propertes of the rope. For chan, R4 was chosen for the study and the followng formulas were appled for ts propertes: MBL =.74 d ( d)/9.81 Page 3 of 5

4 Proceedngs of Conference 8 Korean Socety of Ocean Engneers May 9-3, Cheju, Korea 5,, 45,, 4,,,, 18,, 16,, 5.% WD 7.5% WD (Base Case) 1.% WD 1.5% WD Total Anchor Leg Cost (US$) 35,, 3,, 5,,,, 15,, Mnmum Total Cost (US$) 14,, 1,, 8,, 6,, 5,, Fg 3 Anchor leg cost of averaged cost n HM (base case). 4, 4,,,, Fg 6 Mnmum anchor leg cost vs. requred maxmum offset. Horzontal End Pont Separaton (m) 3,5 3,,5, 1,5 1, Fg 4 Horzontal end pont separaton (base case). Mnmum Total Cost (US$),, 18,, 16,, 14,, 1,, 8,, 6,, 4,,,, FS 1.67 (Base Case) FS=. FS=.5 FS= Fg 7 Mnmum anchor leg cost vs. safety factor. Frequency Farlead Declnaton Angle (deg) Fg 5 Hstogram of top chan declnaton angle (base case). Fgures 6 and 7 present the trend of the mnmum anchor leg cost n the harmony memory as ether requred maxmum offset or factor of safety changes. 5. Conclusons A moorng optmzaton desgn tool usng the harmony search algorthm and a frequency doman global analyss tool was appled to conduct the cost senstvty as a functon of requred maxmum offset and safety factor of the moorng system. The trend of cost-optmal moorng desgn search over 1, teratons was compared. A case study on a permanent turret moorng system for an FPSO n deepwater was conducted. The results show that the safety factor does t sgnfcantly affect the optmum moorng system cost whle the requred maxmum offset could be a bg factor for the total cost of the moorng cost. To better fnd a feasble, cost optmum moorng system, three dfferent types of penalty functons were appled. As shown n the teraton trend of the declnaton angle and horzontal end pont separaton, t s also shown that harmony search s capable of Page 4 of 5

5 Proceedngs of Conference 8 Korean Socety of Ocean Engneers May 9-3, Cheju, Korea fndng optmum desgn values as well as cost-optmum moorng system. References Cunha, MC. and Sousa, J. (1999). "Water Dstrbuton Network Desgn Optmzaton: Smulated Annealng Approach," J. Water Resour. Plann. Mgmt, ASCE, 15(4), pp Fyllng, I. (1997). "Optmzaton of Deepwater Moorng Systems," Proceedngs of the Offshore Medterranean Conference, Ravenna, March Fyllng, I. and Kleven, G. (). "Integrated Optmzed Desgn of Rser and Moorng System for Floatng Producton Vessels," Proceedngs of OMAE Conference, Ocean Engneerng Symposum, New Orleans, USA, February Geem, ZW. (6a). "Optmal Cost Desgn of Water Dstrbuton Networks Usng Harmony Search," Engneerng Optmzaton, Vol 38, No 3, Aprl, pp Geem, ZW. (6b). "Parameter Estmaton for the Nonlnear Muskngum Model Usng BFGS Technque," J. Irrgaton and Dranage Engneerng, ASCE, 13, pp Geem, ZW. (6c). "Improved Harmony Search from Ensemble of Musc Players," Lecture Notes n Artfcal Intellgence, 451, pp Km, JH., Geem, ZW. and Km, ES. (1). "Parameter Estmaton of the Nonlnear Muskngum Model Usng Harmony Search," J. Am. Water Resour. Ass., 37(5), pp Lee, KS. and Geem, ZW. (5). A New Meta-Heurstc Algorthm for Contnuous Engneerng Optmzaton: Harmony Search Theory and Practce," Computer Methods n Appled Mechancs and Engneerng, 194, pp Ryu, S., Duggal, AS., Heyl, CN., and Geem, ZW. (7). "Moorng Cost Optmzaton va Harmony Search," Internatonal Conference on Offshore Mechancs and Arctc Engneerng. Smpson, AR., Dandy, GC., and Murphy, LJ. (1994). "Generc Algorthms Compared to Other Technques for Ppe Optmzaton," J. Water Resour. Plann. Mgmt, ASCE, 1(4), pp Page 5 of 5