# A mathematical programming approach to the analysis, design and scheduling of offshore oilfields

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1 17 th European Symposum on Computer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edtors) 2007 Elsever B.V. All rghts reserved. 1 A mathematcal programmng approach to the analyss, desgn and schedulng of offshore olfelds Rchard J. Barnes and Antons Kokosss Center for Process & Informaton Systems Engneerng School of Engneerng, Unversty of Surrey, Guldford, Surrey, GU2 7XH, U.K. E-mal: Abstract Ths paper presents a general and systematc approach to address decsons n the desgn and operaton of offshore olfelds. The approach s based on the formulaton of mathematcal models that are formulated to accommodate multple producton profles. The profles can be used to assess ether the best strategy or, nstead, possble mplcatons n changng polces durng the operaton. The work decomposes the problem n two stages: the determnaton of the optmum drllng centre and the determnaton of the optmum drllng schedule to meet a specfed producton profle. The proposed method smultaneously addresses and optmzes the operaton of the man producton faclty and an arbtrary number of satellte felds. Felds and wells are selected to gve the overall lowest CAPEX for the development. The method s an mprovement over prevous work and provdes a full optmsaton of lfe-cycle drllng costs. Keywords: Offshore olfeld; Optmsaton; Drllng; Offshore platform, Producton capacty, Lfe cycle cost, Economc analyss. 1. Introducton and problem descrpton Fgure 1 shows the general schematc of offshore feld comprsed by a man feld, F1 and three satellte felds, S1, S2 and S3. The optmum drllng centre s

2 2 Rchard J. Barnes et al. defned as the locaton whch has the lowest total cost of drllng suffcent wells that meet a specfed producton capacty. Such a locaton s affected by the layout of the feld, the depth, locaton and the productvty of ndvdual wells. Moreover, there s an optmum, that s lowest CAPEX, development scenaro n whch the felds are brought nto producton n a sequence where maxmum beneft s acheved from each new feld n order that the target producton profle s met at mnmum CAPEX [4]. S1 Producton or Satellte Platform F1 S2 S3 Ol and gas export to trunk The determnaton of the optmum drllng centre and the most economc producton profle for a feld or group of felds s a complex problem that s based on ncomplete and mprecse data. In order to prepare a robust soluton, t s necessary to nvestgate a large number of dfferent optons of locatons, drllng profles and lfe of feld producton profles. Prevous Fgure 1 Schematc of offshore feld work [1, 2] has presented a well optmsaton method to nvestgate parameters affectng the desgn capacty and the locaton of the man capacty. The work used a sngle heurstc profle for the well producton and a yearly schedulng model to determne drllng schedules and the tmng of satellte producton. Ths paper presents a general and systematc approach to address desgn decsons and support schedulng decsons over the entre horzon. The model s formulated to accommodate multple producton profles that can be used to assess ether the best strategy or possble mplcatons n changng polces durng the operaton. The work decomposes the problem n two stages: the determnaton of the optmum drllng centre and the determnaton of the optmum drllng schedule to meet a specfed producton profle. From ths nformaton an economc analyss of the lfe of the development may be made to gude the operator to the most economc method of developng the feld. It s assumed that there s suffcent knowledge of each reservor and that the potental down-hole well locatons can be defned n terms of three dmensonal coordnates and well productvtes. From ths nformaton, the length of a well drlled from a specfed drllng centre can be calculated as a functon of the ts length. For each year target producton rates are specfed as nput data to descrbe the requred producton profle for each partcular case to be examned. The dfferent profles essentally account for dfferent scenaros. The optmal soluton determnes the drllng sequence requred to acheve the most economc

3 A mathematcal programmng approach to the desgn and schedulng of offshore olfelds. 3 operaton. From the data of well costs, facltes costs and producton profle, an economc analyss can be compared wth other producton profles. In all cases, the models are formulated and solved as MILP problems. 2. Locaton of the drllng centre The mathematcal model s formulated as follows. Gven a set of wells and a set of drllng locatons. For each well locaton (x, y and z coordnates are gven together wth the well productvty) the obectve s dentfy the locaton that corresponds to the mnmum drllng cost. The problem parameters nclude: T = Target feld producton. W, = The cost of drllng well from drllng centre The set of varables consst of: Z = Bnary to select or deselect well. Y = Bnary to select or deselect drllng centre. C, = The actual cost of drllng once and are selected The formulaton of the obectve s then: Cost = C, (1), The obectve functon s to mnmse the cost of drllng suffcent wells from locaton to meet the producton target. Equaton (1) calculates the cost of meetng the producton target from each drllng locaton and determnes the lowest cost locaton. The obectve functon s subect to: C Z + Y 1 * W (2), ( ), Equaton (2) sets the cost of drllng well from locaton to zero, unless both Z and Y are equal to 1. Therefore, only the cost of the wells that are actually drlled from each locaton are totalled n Equaton (1). Z P T (3) Equaton (3) ensures the producton target s met for each drllng locaton. Y = 1 (4) Equaton (4) ensures that there s only one drllng centre. Ths can be relaxed to nvestgate the effect of multple drllng centres. The method descrbed n ths paper was used to determne the optmum drllng centre n two felds of the lterature [1]. The frst feld comprses 29 wells and the second 224 wells. The

4 4 Rchard J. Barnes et al. optmzaton revealed the optmum solutons n 0.1 and 1.6 CPU sec respectvely. 3. Schedulng multple felds The second stage of the nvestgaton s to determne the optmum development schedule o acheve a specfed feld producton profle. The optmsaton task s to determne the drllng sequence and the feld selecton that mnmses the total drllng cost to meet Producton Rate, BPD 120, ,000 80,000 60,000 40,000 20,000 the target producton. The model assumes a man feld and an arbtrary number of satellte felds feedng the man feld facltes. The recoverable reserves, and the locaton and productvty of potental well locatons are fxed parameters whch are used to defne the reservor. These parameters would normally reman constant unless the effect of uncertanty n the reservor were beng nvestgated. The target producton profle descrbes a partcular case beng nvestgated and determnes the speed wth whch the felds are developed. The problem s formulated mathematcally as follows. Gven s a set wells, a set of felds, a set of wells, and a producton tme comprsed by t perods (years). The drllng schedule and annual productons are determned over the feld lfe and over a fxed tme of producton (n years). Problem parameters nclude the: C, = Producton Year Fgure 2 Fgure 2 Producton profle The cost of drllng Well I from the specfed drllng locaton n Feld. T n = Target producton rate for Year n. W n = Potental producton from well n year n. The problem varables nclude: Z t = Bnary varable set to zero except n the year t when a specfc well s drlled. The array descrbes each feld. P,t n, = Actual producton from well n Year n, when drlled n Year t n Feld.

5 A mathematcal programmng approach to the desgn and schedulng of offshore olfelds. 5 The model mnmses the drllng cost over the lfe of the feld, consder wells drlled from all dfferent platforms. The obectve functon s formulated as: Cost = Z * C (5) t,t,, 120, , , ,000 Producton Rate, BPD 80,000 60,000 40,000 Producton Rate, BPD 80,000 60,000 40,000 20,000 20, Producton Year Producton Year Fgure 3: Accelerated producton Fgure 4: Slow developng producton Equaton (5) sums the costs of drllng the wells for each year and each feld or platform. Ths s the obectve functon that must be mnmsed over the lfe of the proect. The obectve functon n (5) s subect to P Z * W (6),t,n,,t,,n t +1 Equaton (6) sets the producton from each well to zero f t s not n operaton or to the specfed producton rate f the well has been drlled. T (7) n P,t,n, t Equaton (7) ensures that the total producton from each feld meets or exceeds the specfed target producton for that year. R P t, n, n t, (8) Equaton (8) ensures that producton from ndvdual felds does not exceed the recoverable reserves for that feld. Fgure 2 shows a typcal producton profle. Producton bulds up n the frst two years, and then remans constant for the plateau perod. Producton then enters the declne perod, contnung untl the revenue from the ol producton no longer exceeds the cost of operatng the feld. The feld s then no longer economc and s abandoned. Fgure 3 shows an accelerated producton programme n whch wells have been pre-drlled

6 6 Rchard J. Barnes et al. before nstallaton of the platform. Contnued drllng mantans the plateau for several years. Producton then declnes relatvely slowly by contnued drllng or workover durng part of the declne perod. Fgure 4 s of a producton profle that bulds up relatvely slow to plateau. Producton begns to rapdly declne wth the cessaton of drllng at the end of plateau producton. The grd spacng may be ncreased to dstrbute the wells over a larger area. Smlarly, an addtonal constrant can be added to lmt the well step out: D M (9) Where: D = Horzontal dstance between drllng centre and well. M = Maxmum permtted step out. The new method has been tested aganst models developed earler [2] and has gven comparable results. To date the new model has not been extended to model declne n well productvty durng feld lfe. 4. Conclusons The paper presents general mathematcal models to enable the optmal development of sngle and multple felds. By decomposng the problem nto two parts: selectng an optmum drllng centre and optmsng the well selecton; the problem complexty s sgnfcantly reduced. Although the problem can become qute large when there are several hundred potental well locatons over a feld lfe of 20 years or more, the problem stll remans well wthn the computatonal capacty of the modern personal computer. The model does not perform an economc analyss on the soluton to permt comparson of the case wth other cases wth dfferent producton profles. It also does not nclude a functon to model the declne n well performance wth producton. However, ths feature could be added n a further refnement. References 1. Barnes, R.J., Lnke, P. and Kokosss, A (2002). Optmsaton of olfeld development producton capacty. ESCAPE 12 proceedngs, The Hague (NL), Barnes, R.J., Kokosss, A. and Shang, Z. An ntegrated mathematcal programmng approach for the desgn and optmsaton of offshore felds. Computers and Chemcal Engneerng (2006). 3. Iyer, R. R., Grossmann, I. E., Vasantharaan, S., & Cullck, A. S. (1998). Optmal Plannng and Schedulng of Offshore Ol Feld Infrastructure Investment and Operaton. Industral and Engneerng chemstry Research, 37, Nero SMS, Pnto JM. A general modellng framework for the operatonal plannng of petroleum supply chans. Internatonal Conference on Foundatons of Computer- Aded Process Operatons, 2003, Computers & Chemcal Engneerng 28 (6-7): , Jun

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