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An MILP method for optimal offshore oilfield gathering system
Ocean Engineering 141 (2017) 25–34
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
An MILP method for optimal offshore oilfield gathering system a
a,⁎
a
b
MARK
a
Haoran Zhang , Yongtu Liang , Jing Ma , Chen Qian , Xiaohan Yan
a National Engineering Laboratory for Pipeline Safety/Beijing Key Laboratory of Urban oil and Gas Distribution Technology, China University of PetroleumBeijing, Fuxue Road No.18, Changping District, Beijing 102249, PR China b University of Calgary, 2500 University Drive, NW, Calgary, Alberta, Canada T2N 1N4
A R T I C L E I N F O
A BS T RAC T
Keywords: Offshore oilfield Gathering pipeline system Optimization Pipeline network topology
Offshore oilfield gathering system plays a key role in oilfield exploration and production process, the rational construction of the gathering system is directly related to the efficiency and profit of the offshore oilfield production. Thus, optimization of the whole gathering system is the key to lower the offshore oilfield production cost, and it also has been one of the major challenges in offshore oilfield production. Many researches have been done on the optimization but pipeline network distribution, treating technical and integrated optimization still remained unsolved. This paper focuses on the common offshore oilfield gathering network construction, taking gathering radius, economic flowrate, terrain obstacles and production technic into consideration, building a mixed integer linear programming (MILP) model, figuring out the globally optimal connection topology, location of center platforms, pressure increment and dehydrating facilities and major parameters of each pipeline, and contributing to further optimal offshore oilfield engineering mode. Last, this paper takes two typical real cases, namely half-offshore and half-continent mode and offshore mode, to test the accuracy of the proposed model. The optimal results indicate the proposed method can lower the general investment and testify the liability and applicability of it.
1. Introduction 1.1. Background Petroleum industry plays a vital role in the modern global economy, owing to the fact that it is the largest source of energy in the world (Sahebi and Nickel, 2014). Across the intervening years, offshore exploration and production have spread around the world, taking place off the coasts of Africa, Asia, Central and South America, and Europe (Gramling and Freudenburg, 2006). Offshore gathering pipeline system collects, disposes and transfers the produced liquid and plays a key role in the whole offshore production system (Kawsar et al., 2015; Wang et al., 2017). The construction of offshore gathering system costs a huge part of the oilfield production investment (Kearney, 2010; Tsibulnikova et al., 2015). The rational construction of it is directly related to the efficiency and profit of the offshore oilfield production. Thus, the optimization of the whole gathering system is the key to lower the offshore oilfield production cost, and it is also one of the major challenges in offshore oilfield production (Liu et al., 2015). Offshore oilfield gathering pipeline system optimization contains optimal well groups division, geometric center of points set location (Li et al., 2011), minimum spanning tree of graph theory (Rothfarb et al.,
⁎
Corresponding author. E-mail address: [email protected] (Y. Liang).
http://dx.doi.org/10.1016/j.oceaneng.2017.06.011 Received 3 November 2016; Received in revised form 27 May 2017; Accepted 5 June 2017 0029-8018/ © 2017 Elsevier Ltd. All rights reserved.
1970), shortest route (Knoope et al., 2014; Marcoulaki et al., 2012) and many other sub questions. Most of the sub questions are typical nondeterministic polynomial complete (NPC) models. Usually these sub questions are coupled, and considering the direction of pipeline (Dan and Williams, 2015; Schwarz et al., 2015), topology, submarine geomorphology and obstacles (Haneberg, 2015; Rocha et al., 2015) and production technical, thus the offshore oilfield gathering pipeline optimization can be very complex. Moreover, the current models and methods are unable to solve complex connections and general and globally optimal results. This paper focuses on the common offshore oilfield gathering network construction, taking gathering radius, submarine geomorphology and obstacles, and production technic into consideration, building an MILP model, figuring out the global connection topology, center platform location, pressure increment and dehydrating facilities and major parameters of each pipeline, and contributing to further optimal offshore oilfield engineering mode. 1.2. Related work Since the offshore oil field gathering system is complex, many scholars have carried out researches on different aspects of this issue. In the work of And et al. (1998), he employed a general objective
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Nomenclature
Rmax RP max
Acronyms
Discrete parameters
NPC problem Non-deterministic Polynomial Complete problem. NPV Net Present Value. MIP Mixed Integer Programming. MILP Mixed-Integer Linear Programming. MINLP Mixed-Integer Non-Linear Programming. GDP Gross Domestic Product.
FIPx, y FDDx, y FWPx, y
Sets and indices
FPFx, y, r
(x, y), (rxx, y, r , ryx, y, r ) ∈ XY Set of gird coordinate. r , rrr ∈ R Set of connection direction. d∈D Set of pipe diameter. v∈V Set of flowrate classes.
CPFQ CPv CPPQ CBCx, y CDd LDx, y, r
M γ Q PV max v Q PV min v Q DF max d Q DF min d Q WPx, y
Platform construction binary variable. FIPx, y = 1 if (x, y) is suitable for constructing a platform, or else, FIPx, y = 0 . Onshore terminal binary variable. FDDx, y = 1 if (x, y) is onshore terminal, or else, FDDx, y = 0 . Wellhead location binary variables. FWPx, y = 1 if (x, y) is wellhead, or else, FWPx, y = 0 . Pipeline installation condition binary variable. FPFx, y, r = 1 if pipeline could start from (x, y) to the adjacent node along direction r, or else, FPFx, y, r = 0 .
Continuous variables
Q Dx, y, r Q Px, y Q PFx, y Q DDx, y Q PPx, y Hx, y
Continuous parameters
CFx, y CPFv
wellhead. Maximum gathering radius. Maximum gathering radius increment powered by pumps.
Platform construction cost at (x, y). Separating facilities cost when separating liquid in volume flowrate class v . Dehydrating cost for a volume crude oil. Pressure increment facilities cost when transferring liquid in volume flowrate class v . Pressure increment cost for a volume crude oil. Center platform construction cost at (x, y). Construction unit price of pipeline with diameter d . Connecting distance from (x, y) to the adjacent node along direction r . A maximum value Dehydrating efficiency Upper bound of flowrate class v . Lower bound of flowrate class v . Upper bound of economic flowrate of pipeline with diameter d . Lower bound of economic flowrate of pipeline with diameter d . Output of wellhead (x, y). Q WPx, y = 0 if (x, y) is not a
Flowrate from (x, y) to the adjacent node along direction r . Platform receiving flowrate at (x, y). Free water volume separated at (x, y). Final receiving flowrate at (x, y). Flowrate at pressure increment facility (x, y). Equivalent connection length at (x, y).
Binary variables
BFx, y BCx, y BPFx, y, v
BPx, y, v
BDx, y, r , d
Platform construction binary variable. BFx, y = 1 if platform is constructed at (x, y), or else, BFx, y = 0 . Center platform construction binary variable. BCx, y = 1 if platform is constructed at (x, y), or else, BCx, y = 0 . Dehydrating facility construction binary variable. BPFx, y, v = 1 if dehydrating facility is constructed at (x, y), or else, BPFx, y, v = 0 . Pressure increment facility construction binary variable. BPx, y, v = 1 if pressure increment facility is constructed at (x, y), or else, BPx, y, v = 0 . BDx, y, r , d = 1 if pipeline with diameter d could start from (x, y) to adjacent node along direction r , or else, BDx, y, r , d = 0 .
considered the optimal layout problem for a pipeline of given length in the presence of uncertainties in the failure rates of its constituent parts (i.e. pipes and joints). Wu et al. (2007) established a mathematical optimization model for the problem of minimizing the cost of pipelines incurred by driving the gas in a distributed non-linear network, based on distribution gas pipeline networks which had a steady demand. The decision variables included the selection of the pipes’ diameter, pressure drops at each node of the network, and mass flow rate at each pipeline leg. Ruan et al. (2009) presented a model that minimized the total pipeline and compressors investment cost for onshore natural gas transmission pipelines, and proposed a rank-optimization method to solve the model. Marcoulaki et al. (2012) established a nonlinear programming model for pipeline route optimization, which considered process constraints and was solved by stochastic optimization method. Zhang et al. (2015) developed several programming models respectively for multiple connection modes of onshore gathering networks and an improved genetic algorithm was used to figure out the model. Then Duan et al. (2016) proposed a two-stages method based on Zhang et al. (2015), considering geographic factors. Despite the comprehensive coverage of network connection modes, those methods are hard to ensure the result calculated by intelligence algorithms has global optimality. Yet it is difficult to guarantee the optimality of the results obtained by intelligent algorithms as the model scale increased (Jr
function of MILP model that optimized a selected economic indicator (e.g., net present value) and incorporated the nonlinear reservoir performance, surface pressure constraints, and drilling rig resource constraints. Carvalho and Pinto (2006) proposed a mixed integer programming (MIP) with the discrete and continuous decisions to maximize the net present value and took the pressure of each reservoir. Gupta and Grossmann (2012) solved the offshore oilfield development problem based on the multi-period non-convex mixed-integer nonlinear programming (MINLP) model aiming at obtaining the maximizing total net present value (NPV) for long-term planning horizon. As for the topological optimization of natural gas transmission networks, Kabirian and Hemmati (2007) proposed an MINLP model combining installation and operating costs, to develop optimal network structures by selecting the type and location of pipeline and compressor stations. Sahebi and Nickel (2014) came up with a mixed integer model to design the oilfield development and plan crude oil transportation problems. For the nonconvex mixed-integer nonlinear optimization problems, Rose et al. (2016) established MINLP model for operating a single station and discussed several continuous reformulations of the problem. However, researchers mentioned above had not considered geomorphology or process constraints. Intelligent algorithms have been applied to solve complex topology structures of oil and gas gathering networks. Marseguerra et al. (2004)
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center platform location, pressure increment and dehydrating facilities location, parameters and route of pipes and compares the optimal result with that of current algorithms.
et al., 2011; Vieira et al., 2010). Furthermore, intelligent algorithms could easily converge to the locally optimal solution as a result of the strong randomness, thus the calculation results need to be further discussed. Some scholars have tried to deal with network structure topology optimization by heuristic algorithms. Rothfarb et al. (1970) put forward three fundamental issues for topology optimization of offshore natural gas pipeline networks: (1) selection of pipe diameters in a specified pipeline network to minimize the sum of investment and operation costs; (2) selection of minimum-cost network structures, given gas-field locations and flow requirements; (3) optimal expansion of existing pipeline networks to include newly discovered gas fields. And techniques were attempted to put into practice, which were incorporated procedures for globally optimizing pipeline diameters for fixed tree structures and heuristic procedures for generating lowcost structures. But geomorphology constraints were not taken into consideration. Dolan et al. (1989) combined the approach of Rothfarb et al. (1970) with simulated annealing and came up with a different approach to the pipeline network design problem. Recently，Rosenthal (2010) studied the solution of the pipe diameter problem by non-serial dynamic programming. Baumrucker and Biegler (2010) developed a mathematical program with equilibrium constraints (MPECs) approach for efficient operation of gas pipelines. Wang et al. (2012) established a mathematical model for topology optimization of the submarine cluster structures and proposed a heuristic algorithm based on the hyperlink matrix. Whereas factors such as terrain and obstacles were not taken into account, and the proposed algorithm was confined to the specific structure optimization of pipe networks. Brimberg et al. (2003) built up a mixed integer programming model (MILP) for the optimization of nearshore pipeline network arrangement and pipeline type. And the tabu search and variable neighborhood search were coupled together to solve the model. Dey et al. (2004) developed a risk-based maintenance model using a combined multiple-criteria decision-making and weight method for offshore oil and gas pipelines. Lucena et al. (2014) dealt with the route optimization of subsea gathering pipelines by establishing a mathematical programming model, considering the constraints of subsea obstacles. The evolutionary algorithm was determined to solve the model. Since only the line selection between two points could be carried out by the model, it failed to be directly applied for global optimization of pipeline networks. However, the heuristic algorithms mentioned above have poor universal application for it only aims to the specific problems subjected to the model constraints. Thus, current models and algorithms cannot solve the complex connection and integral solution problem. This paper builds an MILP model with submarine obstacles and production technic as constraints for common offshore oilfield pipeline network connection, and figures out the globally optimal topology,
2. Methodology 2.1. Problem description Offshore oilfield production usually sets wellhead platforms or center platforms at the wellheads. In this paper, the wellhead platforms can be defined as the satellite platforms which connect to the center platform by stellated connection mode and there is no connection among wellhead platforms. Since the deck of the wellhead platform is small, the pressure increment and processing facilities are not allowed to be installed. The center platforms can be connected to each other to receive the produced liquid from wellhead platforms. Contrary to the wellhead platform, the deck of the center platform is larger, which can place the pressure increment and processing facilities. Platforms are connected by submarine pipelines. When installing the submarine pipes, designers should consider the submarine terrain and obstacles, install on ideal geological conditions with smooth slope and avoid trench and faults. Meanwhile, if two destinations are away from each other, pressure increment facilities should be taken into consideration. If the produced liquid at wellheads contains a large amount of water, dehydrating facilities should be taken into consideration as well. Offshore oilfield engineering modes include half-offshore and halfcontinent mode and offshore mode, as shown in Fig. 1. In the first mode, offshore produced liquid will first be separated into oil and water and then transferred to onshore terminal for further process. Installing submarine pipes cost a lot, thus this mode can only be applied to a short distance offshore production block. Accordingly, offshore production mode can be applied to a long distance offshore oilfield. In this mode, FPSO is used for oil processing and storage instead of onshore terminal. The essence to optimize offshore oilfield gathering system is the selection and optimization of wellhead position, platform location, network distribution, pipe diameter and length, pressure increment and dehydrating facilities location. The model adopts the discrete mesh division by which the study area is divided into a number of sub-squares. The 16 node-type connection structure is applied to build up the corresponding constraint equations, function objective and the programming model for each sub-square. As shown in Fig. 2, R is the number set of connection direction between node and the subscript is represented by r while rrr as the opposite direction of r . XY is the coordination set of all the mesh nodes in study area. Supposing node (x′, y′) as the terminal of node (x, y) going through a distance along the direction r , define x′ = rxx, y, r and y′ = ryx, y, r . Similarly, node (rxx, y, rrr , ryx, y, rrr ) is obtained by node (x, y) along the opposite direction of r .
Fig. 1. Offshore oilfield gathering system. (a) half-offshore and half-continent mode (b) offshore mode.
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2.3. MILP model Based on MILP model structures, an optimization model for offshore oilfield gathering system is proposed in this paper, which aims to work out a offshore oilfield gathering system with the least construction cost under the premise of production and hydraulic constraints. Combined with specific actual data, the optimization issue of offshore oilfield gathering system can be transformed into an MILP mathematical model, and then solved by mature MILP solver. The optimal construction scheme of offshore oilfield gathering system can be obtained. To intuitively show the proposed model, the following compact form is presented. The detailed content will be elaborated in Section 3.
min F ( pi , pl , pr , Qn ) pi, pl, pr , Qn
s.t.φ ( pl , pr , Qn ) ≤ 0 ψ ( pi , Qp ) ≤ 0 ϕ ( pi , Qp , Qn ) = 0 ξ ( pi ) ≤ 0
(1)
where: pi represents design variables of submarine pipelines. pl represents design variables of platforms. pr represents design variables of processing facilities. Qn represents variables of node flowrate. Qp represents variables of pipeline flowrate. F represents objective function. φ represents universal constraints of platform construction. ψ represents universal constraints of pipeline flowrate. ϕ represents universal constraints of flowrate balance. ξ represents universal constraints of pipeline construction. As seen from Eq. (1), the objective function of the optimization model of offshore oilfield gathering system is associated with pipelines, platforms, processing facilities, and processing capacity of the system. There are four types of constraints in the optimization model. The first type is constraints of platform construction φ , which mainly describe the construction location of platforms and the specification of processing facilities. Those constraints involve pl , pr and Qn . The second type is constraints of pipeline flowrate ψ , which mainly describe the relationship between size of pipeline and pipeline flowrate. Those constraints are related with pi and Qp . The third type is constraints of flowrate balance ϕ , which mainly describe the flowrate of each node with specific pipeline connection structures and the relationship between each pipeline flowrate. The last type is constraints of pipeline construction ξ , which mainly describe the constraints on pipeline connection structure due to gathering radius limit and are related with pi .
Fig. 2. Mesh division and direction.
2.2. Model requirements The model is formulated as MILP and the optimization is executed using GUROBI. A detailed offshore oilfield gathering pipeline system construction scheme can be obtained by solving the model. Given: 1. well group information: well group location, well group output, water cut of produced liquid 2. obstacle information 3. gathering radius 4. construction unit price: pipe unit price (of different diameters), platform construction unit price, dehydrating facilities unit price Determine: 5. pipeline connection mode 6. pipeline diameter based on economic flowrate 7. pipeline flow direction 8. center platform location Objective: The objective is to minimize the total costs, including pipeline costs, platform and affiliated facilities construction costs, pressure increment and dehydrating facilities costs and the cost of pressure increment and dehydrating process, and to work out a detailed offshore oilfield gathering pipeline system construction scheme under various operational and technical constraints. In order to solve the model more efficiently, assuming: 9. To make sure the designed gathering system can work safely, this paper takes gathering radius as the model constraint. If the gathering and transferring distance is less than the gathering radius, this paper assumes the whole system meets the hydraulic and thermal requirements. 10. During the submarine pipeline designing process, the first step is primarily selecting several pipe diameters based on economic flowrates, then taking flow, mechanic and transfer conditions into consideration and determining the exact diameter. This paper selects the final diameter based on economic flowrates. The selected diameter should be further testified under the in sit condition. 11. This paper assumes the pressure increment facilities have enough power to transfer the oil till the terminal, and the produced oil just can go through only one dehydrating and pressure incrementing process.
3. Mathematical formulations 3.1. Objective function The objective function is to work out the offshore oilfield construction scheme with lowest cost under each given constraint. Total costs include platform and its affiliated facilities construction costs and pipeline construction costs. Platforms and their affiliated facilities construction costs include platform construction costs, dehydrating and pressure increment facilities costs. The latter costs depend on the oil volume they processed.
f1 =
∑ ∑ x
y
⎛ ⎜⎜CFx, y BFx, y + ⎝
∑
CPFv BPFx, y, v + CPFQ Q Px, y
v
⎞ + ∑ CPv BPx, y, v + CPPQ Q PPx, y + CBCx, y BCx, y⎟⎟ ⎠ v (x, y) ∈ XY , v ∈ V
(2)
Pipeline construction costs depend on pipeline diameter and length. 28
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f2 =
Boosted flowrate equals to platform receiving flowrate if there are no process facilities.
∑ ∑ ∑ ∑ CDd LDx,y,r BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D x
y
r
(3)
d
⎛ ⎜⎜1 − ⎝
3.2. Constraints of platform construction
∑ BPFx,y,v M + QPPx,y ≤ QPx,y (x, y) ∈ XY , v ∈ V v
(18) Boosted flowrate equals to the platform receiving flowrate minus dehydrating flowrate if there is a process facility.
There must be a platform at the well head.
⎛ ⎜⎜1 − ⎝
(5)
The receiving flowrate must be zero if there is no platform.
BFx, y M ≥ Q Px, y (x, y) ∈ XY
v
⎛ ⎞ ⎜⎜∑ BPx, y, v − 1⎟⎟ M − ⎝ v ⎠
(4)
FWPx, y ≤ BFx, y (x, y) ∈ XY
⎠
v
(17)
The platform construction binary variable must equal to 0 if this spot is not suitable for setting a platform. FIPx, y denotes the suitability of setting a platform and FIPx, y = 1 if this spot is suitable for setting a platform. BFx, y denotes platform construction binary variable. If this spot is suitable for setting a platform, then BFx, y = 1, or else, BFx, y = 0 .
BFx, y ≤ FIPx, y (x, y) ∈ XY
⎞
∑ BPx,y,v⎟⎟ M + ∑ BPFx,y,v M + QPPx,y ≥ QPx,y (x, y) ∈ XY , v ∈ V
⎞
⎛
⎠
⎝
⎞
∑ BPx,y,v⎟⎟ M + ⎜⎜1 − ∑ BPFx,y,v⎟⎟ M + QPPx,y ≥ QPx,y − QPFx,y (x, y) v
⎠
v
(19)
∈ XY , v ∈ V
(6)
⎛ ⎞ ⎛ ⎞ ⎜⎜∑ BPx, y, v − 1⎟⎟ M + ⎜⎜∑ BPFx, y, v − 1⎟⎟ M + Q PPx, y ≤ Q Px, y − Q PFx, y (x, y) ⎝ v ⎠ ⎝ v ⎠
The receiving flowrate equals to the sum of produced flowrates at each node and the influx flowrate from other nodes.
∑ QDrxx,y,r,ryx,y,r ,rrr + (1 − BFx,y) M + Q WPx,y ≥ QPx,y (x, y), (rxx,y,r , ryx,y,r )
(20)
∈ XY , v ∈ V
r
The constraints of pressure increment facilities are the same as those of dehydrating facilities.
(7)
∈ XY , r , rrr ∈ R
∑ QDrxx,y,r,ryx,y,r ,rrr + (BFx,y − 1) M + Q WPx,y ≤ QPx,y (x, y), (rxx,y,r , ryx,y,r )
(1 − BPx, y, v ) M + Q PV max v ≥ Q PPx, y (x, y) ∈ XY , v ∈ V
(21)
(BPx, y, v − 1) M + Q PV min v ≤ Q PPx, y (x, y) ∈ XY , v ∈ V
(22)
r
∈ XY , r , rrr ∈ R
(8)
Dehydrating and pressure increment facilities must be installed on a platform.
∑ BPFx,y,v ≤ BFx,y (x, y) ∈ XY , v ∈ V v
3.3. Constraints of pipeline and node flowrate Transferring flowrate must equal to zero if there are no pipes between two spots.
(9)
Dehydrating flowrate must equal to zero if there are no dehydrating facilities at this spot
∑ BPFx,y,v M ≥ QPFx,y (x, y) ∈ XY , v ∈ V v
∑ BDx,y,r,d M ≥ QDx,y,r (x, y) ∈ XY , r ∈ R, d ∈ D
There must be no pipes in between if the transferring flowrate equals to zero.
(10)
Dehydrating flowrate equals to processing flowrate times dehydrating efficiency.
⎛ ⎜⎜1 − ⎝
⎞ ∑ BPFx,y,v⎟⎟ M + QPx,y γ ≥ QPFx,y (x, y) ∈ XY , v ∈ V ⎠ v
⎛ ⎞ ⎜⎜∑ BPFx, y, v − 1⎟⎟ M + Q Px, y γ ≤ Q PFx, y (x , y) ∈ XY , v ∈ V ⎝ v ⎠
Q Dx, y, r M ≥
∑ BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D
Determine transferring flowrate classes.
(11)
(12)
(1 − BPFx, y, v ) M + Q PV max v ≥ Q Px, y (x, y) ∈ XY , v ∈ V
(13)
(BPFx, y, v − 1) M + Q PV min v ≤ Q Px, y (x, y) ∈ XY , v ∈ V
(14)
(1 − BDx, y, r , d ) M + Q DF max d ≥ Q Dx, y, r (x, y) ∈ XY , r ∈ R, d ∈ D
(25)
(BDx, y, r , d − 1) M + Q DF min d ≤ Q Dx, y, r (x, y) ∈ XY , r ∈ R, d ∈ D
(26)
Final receiving flowrate of any node except onshore terminal nodes must equal to zero.
Q DDx, y ≤ FDDx, y M
(x, y) ∈ XY
Q WPx, y +
∑ QDrxx,y,r,ryx,y,r ,rrr = QDDx,y + ∑ QDx,y,r + QPFx,y (x, y), r
r
(rxx, y, r , ryx, y, r ) ∈ XY , r , rrr ∈ R
v
(28)
The sum of transferring flowrates at onshore terminal nodes equals to the sum of all production flowrates at wellheads minus the free water flowrates at each dehydrating node.
(15)
Boosted flowrate must equal to zero if there are no pressure increment facilities.
∑ BPx,y,v M ≥ QPPx,y (x, y) ∈ XY , v ∈ V
(27)
The sum of production flowrates at wellheads and influx flowrates from adjacent nodes equal to the sum of final receiving flowrate, the out flux flowrate of this node and the free water flowrate after dehydrating process.
Pressure increment facilities must be installed on a platform.
v
(24)
d
There are different kinds of classes for dehydrating facilities, and in virtue of their flowrate limits, the corresponding facilities should be determined based on the real flowrates. If the platform has to construct dehydrating facility (When ∑v BPFx, y, v = 1) and the receiving flowrate Q Px, y is in class v′ (When ∑v BPFx, y, v = 1 and Q PV min v ′ ≤ Q Px, y ≤ Q PV max v ′), the processing capacity class of dehydrating facility must be equal to v′(BPFx, y, v ′ = 1).
∑ BPx,y,v ≤ BFx,y (x, y) ∈ XY , v ∈ V
(23)
d
(1 − FDDx, y ) M +
∑ ∑ Q WPx,y − ∑ ∑ QPFx,y ≥ ∑ QDrxx,y,r,ryx,y,r ,rrr (x, y), x
(16)
y
x
y
r
(rxx, y, r , ryx, y, r ) ∈ XY , r , rrr ∈ R 29
(29)
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(FDDx, y − 1) M +
∑ ∑ Q WPx,y − ∑ ∑ QPFx,y ≤ ∑ QDrxx,y,r,ryx,y,r ,rrr (x, y), x
y
x
y
increase the transferring distance of the gathering system. Equivalent largest connecting distance has a maximum value based on the efficacious workaround of pumps.
r
(rxx, y, r , ryx, y, r ) ∈ XY , r , rrr ∈ R
(30)
−RP max ≤ Hx, y
One node can have up to one flow direction and one route connected with the adjacent node. Onshore terminal nodes must have no further connection.
1 − FDDx, y ≥
∑ ∑ BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D r
d
(x, y) ∈ XY
(41)
Each route can only have one pipe.
∑ BDx,y,r,d + ∑ BDrxx,y,r,ryx,y,r ,rrr,d ≤ 1(x, y), (rxx,y,r , ryx,y,r ) ∈ XY , r , r d
d
(31)
rr ∈ R, d ∈ D
(42)
Wellhead nodes must have a further connection.
FWPx, y ≤
∑ ∑ BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D r
d
4. Results and discussion
(32)
A platform has a maximum amount of further connecting pipes.
(1 − BFx, y ) M + NP ≥
The proposed method can be applied to the optimization of offshore oilfield gathering system for half-offshore and half-continent mode and offshore mode. This paper testifies the applicability and accuracy of the method by using the following two cases. MATLAB R2014a is taken as programming environment and GUROBI Optimizer is chosen to solve the proposed MILP model. GUROBI Optimizer is a state-of-the-art solver for mathematical programming. The solvers in GUROBI Optimizer are designed from the ground up to exploit modern architectures and multi-core processors, using the most advanced implementations of the latest algorithms. There is the built-in improved branch and bound algorithm solving MILP models, which is a search algorithm for globally optimal solution. Thus, the globally optimal design solution of offshore oilfield gathering system can be obtained by the proposed model and GUROBI Optimizer.
∑ ∑ BDrxx,y,r,ryx,y,r ,rrr,d (x, y), (rxx,y,r , ryx,y,r ) ∈ XY , r r
d
(33)
, rrr ∈ R, d ∈ D
One node can only have up to one other node transferring liquid if this node is neither wellheads nor onshore terminal.
BFx, y M + FDDx, y M + 1 ≥
∑ ∑ BDrxx,y,r,ryx,y,r ,rrr,d (x, y), (rxx,y,r , ryx,y,r ) r
d
∈ XY , r , rrr ∈ R, d ∈ D
(34)
Connection binary variable must equal to zero if this spot is unsuitable for constructing pipes.
FPFx, y, r ≥
∑ BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D d
(35) 4.1. Example 1
3.4. Constraints of pipeline construction
Taking a offshore 15 km × 15 km block for instance. Given 8 well groups, each has certain amount of wellheads. Offshore drilling and production are usually based on platform, all wellheads are collected to the platform as the center. As shown in Fig. 3, the grey area indicates the obstacles and is unsuitable for installing pipeline and stations. The black dots in the figure indicate the well group locations, and output of well group is shown in Table 1. The red square indicates the onshore terminal, and all produced liquid must be transferred to the onshore terminal. Costs of wellhead and center platforms are shown in Table 2. Only the center platform can receive oil from other platforms, and there must be a platform at wellhead. Different pipeline diameters and
Equivalent largest connecting distance of one node equals to zero if this node has no connection with other nodes.
Hx, y ≤
∑ ∑ BDx,y,r,d M + ∑ ∑ BDrxx,y,r,ryx,y,r ,rrr,d M (x, y) r
d
r
d
(36)
∈ XY , r ∈ R, d ∈ D
Equivalent largest connecting distance of one node equals to the sum of equivalent largest connecting distance of the previous node and the connecting distance if there are no pressure increment facilities at this node.
Hx, y ≤ Hrxx, y, r , ryx, y, r + LDrxx, y, r , ryx, y, r , rrr +
∑ BPx,y,v M v
⎛ + ⎜⎜1 − ⎝
⎞ ∑ BDrxx,y,r,ryx,y,r ,rrr,d ⎟⎟ M ⎠ d
Hx, y ≥ Hrxx, y, r , ryx, y, r + LDrxx, y, r , ryx, y, r , rrr −
(37)
∑ BPx,y,v M v
⎛ ⎞ + ⎜⎜∑ BDrxx, y, r , ryx, y, r , rrr , d − 1⎟⎟ M ⎝ d ⎠
(38)
(x, y), (rxx, y, r , ryx, y, r ) ∈ XY , r , rrr ∈ R, d ∈ D Equivalent largest connecting distance of a wellhead node must be a positive value if there are no pressure increment facilities attached.
Hx, y + (1 − FWPx, y ) M ≥ −∑ BPx, y, v M v
(x, y) ∈ XY (39)
Equivalent largest connecting distance of any node must be less than the largest gathering radius.
Hx, y ≤ Rmax
(x, y) ∈ XY
(40)
Equivalent largest connecting distance of one node could be less if there are pressure increment facilities at this node, which could
Fig. 3. Oilfield wellhead and onshore terminal position of example 1.
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Table 1 Well group output of example 1.
Table 4 Pressure increment and dehydrating facilities costs.
No.
Output (m3/d)
No.
Output (m3/d)
processing capacity class
Ⅰ
Ⅱ
Ⅲ
Ⅳ
Ⅴ
1 2 3 4
2480 1390 2800 3680
5 6 7 8
2340 3180 2460 2310
Upper flowrate limit of pressure increment facilities (m3/d) Lower flowrate limit of pressure increment facilities (m3/d) Pressure increment facilities cost (million dollar) Upper flowrate limit of dehydrating facilities (m3/d) Lower flowrate limit of dehydrating facilities (m3/d) Dehydrating facilities costs (million dollar)
14,000
18,000
22,000
24,000
28,000
10,000
14,000
18,000
22,000
24,000
14.57
16.03
17.48
18.94
21.86
14,000
18,000
22,000
24,000
28,000
10,000
14,000
18,000
22,000
24,000
29.14
30.60
32.05
33.51
36.43
Table 2 Platform costs. Category
Cost (thousand dollar)
Infrastructure cost Unit price with depth Center platform
48,663.8 1457 80,135
Table 5 The property of the produced liquid.
the corresponding economic flowrate classes are shown in Table 3. Pressure increment and dehydrating facilities can only be installed on the center platform, and there must be supporting facilities such as increased floor space and electricity. The corresponding costs are shown in Table 4. The processing flowrate class represents the facility processing capacity which keeps proportional to the flowrate. There are five different kinds of classes for pressure increment and dehydrating facilities, and in virtue of their flowrate limits, the corresponding facilities should be determined based on the real flowrates, as shown in constraints 13,14,21,22. The property of the produced liquid is shown in Table 5. The results are shown in Fig. 4. The yellow dots and green dots respectively indicate the locations of satellite platforms and center platforms. And the blue dots represent center platforms equipped with pressure increment and dehydrating facilities after optimization on the original center platforms. The pipeline network after optimization meets all constraints requirements. The pipe length of each pipeline diameter is shown in Table 6. The implementation result shows that the center platform should be constructed at dot 8 and the pressure increment facilities (classⅠ) and dehydrating facilities (classⅢ) are needed. The main reason is that the distance between the dot 8 and the terminal is so long that the wellhead pressure is not enough, thereby needing to build the pressure increment facilities. Meanwhile, it is not economic to transport the crude oil with free water to the terminal on account of the high water content in the produced liquid. Therefore, the dehydrating facilities are necessary for the free water separation. In the light of the existing topology of the pipeline network, PIPESIM was used for hydrothermal check. The modelling interface of PIPESIM is shown in Fig. 5. PIPESIM is a set of simulation calculator of steady-state multiphase flow developed by
Example
Free water ratio/%
Density / (kg m−3)
Viscosity / (mPa s)
Initial boiling point /℃
Wax content / %
Example 1 Example 2
46 53
938.2 937.4
184.1 174.5
148 142
7.42 9.38
Schlumberger. The built-in black oil model (Trangenstein and Bell, 1989) of the software was applied to simulation of oil liquid and the built-in Beggs-Brill equation to calculation of pressure drop. The dot pressure is shown in Fig. 6, which indicated the result can satisfy the requirement. 4.2. Example 2 Taking a offshore 15 km × 15 km block for instance. Given the location and output of 14 well groups as shown in Fig. 7, this block has rugged and complex terrain. The grey area indicates the obstacles and is unsuitable for installing pipeline and stations. The black dots in the figure indicate the well group locations, and the output of well group is shown in Table 7. The red square indicates the position of FPSO. All produced liquid must be transferred to the FPSO. The platform costs, pipeline data and the pressure increment and dehydrating facilities costs are the same as example 1, shown in Tables 2–4. The property of the produced liquid is shown in Table 5. The results are shown in Fig. 8. The pipeline network after optimization meets all constraints requirements. The pipe length of each pipeline diameter is shown in Table 8. The implementation result shows there is no need for pressure increment and dehydrating facilities. It is analyzed that the pipeline of this block is short and the pressure increment is unnecessary as the
Table 3 Pipeline data.
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Fig. 6. Dot pressure of the network in example 1. Note: Pipe 8-0 denotes the pipe between node 8 and 0 (terminal).
Fig. 4. Optimal result of offshore oilfield gathering system of case one. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 6 Pipe length of example 1. Diameter
6 in.
8 in.
10 in.
12 in.
14 in.
Length (km)
12.1
3.0
0
7.8
0
wellhead pressure can satisfy the liquid lift to the terminal FPSO. Meanwhile, there are dehydrating facilities on the terminal FPSO for unified processing thus they are unnecessary to be set on platforms. In the light of the existing topology of the pipeline network, the PIPESIM modelling interface is shown in Fig. 9. The dot pressure is shown in Fig. 10, which indicated the result can satisfy the requirement.
Fig. 7. Oilfield wellhead and FPSO position of example 2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
heuristic algorithm for deep-water gathering system. The problem can be approximately perceived as that to be solved in this paper. Although the heuristic algorithm can quickly solve the model, it isn’t a global search algorithm and thus the optimality of the calculational result still need further discussion. Zhang et al. (2015) adopted an improved genetic algorithm to optimize the topological structure of coal-bed methane gathering pipeline networks. And the algorithm, which is used
4.3. Method comparison According to literatures, there are few researches on optimization of offshore oilfield gathering system. The corresponding modification to other algorithms for gathering pipeline optimization can also solve this kind of problem. For instance, Wang et al. (2012) put forward a
Fig. 5. Modelling interface of PIPESIM in example 1.
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Table 7 Well group output of example 2. No.
Output (m3/d)
No.
Output (m3/d)
1 2 3 4 5 6 7
1520 2480 6110 2800 3110 3680 2340
8 9 10 11 12 13 14
3180 2460 1310 4890 5630 2460 2310
Fig. 10. Dot pressure of the network in example 2.
for solving the connection mode of combination of well tandem and valve, can be modified and applied to optimize the offshore oilfield gathering system. The genetic algorithm is a global search algorithm but it will easily converge to the locally optimal solution if the model has strong nonlinearity. Duan et al. (2016) proposed a two-stages method based on Zhang et al. (2015), considering geographic factors. Firstly, he applied the improved genetic algorithm to solve the twodimensional optimal topology of pipeline networks. And then based on this, he took the three-dimensional terrain into account and used the ant colony algorithm for further resolution. The method can work out the optimization considering complex terrain, but it is still easy to converge to the locally optimal solution. In order to testify the optimization effect of the proposed method, this paper takes methods from Wang et al. (2012), Zhang et al. (2015) and Duan et al. (2016) to carry out the same example. On account of the disadvantage of three methods referred above, there is a penalty function added solving the problem to make the comparison more objectively. The calculation results are shown in Fig. 11. In example one, the proposed method can save 7.1 million dollar, 21.5 million dollar and 12.0 million dollar for investment compared with the others respectively. While in example two, 8.8 million dollar, 15.1 million dollar and 10.0 million dollar can be saved. Since the algorithm is the global optimization, it avoids the poor applicability, the unstable calculation results and the deviation in calculation effects in the previous intelligence algorithm and heuristic algorithm. The algorithm can be easily applied to solving optimization models of offshore oilfield gathering system.
Fig. 8. Optimal result of offshore oilfield gathering system of example 2.
Table 8 Pipeline length of example 2. Diameter
6 in.
8 in.
10 in.
12 in.
14 in.
Length(km)
12.1
15.9
4.8
0
0
Fig. 11. Comparison of three algorithms. Fig. 9. Modelling interface of PIPESIM in example 2.
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Assessment of dropped object risk on corroded subsea pipeline. Ocean Eng. 106, 329–340. Kearney, O.P., 2010. Production Taxation and Offshore Oil Investment: Evidence from the Gulf of Mexico. Knoope, M.M.J., Raben, I.M.E., Ramírez, A., Spruijt, M.P.N., Faaij, A.P.C., 2014. The influence of risk mitigation measures on the risks, costs and routing of CO2 pipelines. Int. J. Greenh. Gas Control 29, 104–124. Li, Z., Sun, Y., Zhang, Z., Liu, J., 2011. A global optimization method based on genetic algorithms for gas gathering pipeline network in a gas field. Nat. Gas. Ind. 31, 86–89. Liu, Y., Li, J., Wang, Z., Wang, S., Dong, Y., 2015. The role of surface and subsurface integration in the development of a high-pressure and low-production gas field. Environ. Earth Sci. 73, 5891–5904. Lucena, R.R.D., Baioco, J.S., Lima, B.S.L.P.D., Albrecht, C.H., Jacob, B.P., 2014. Optimal design of submarine pipeline routes by genetic algorithm with different constraint handling techniques. Adv. Eng. Softw. 76, 110–124. Marcoulaki, E.C., Papazoglou, I.A., Pixopoulou, N., 2012. Integrated framework for the design of pipeline systems using stochastic optimisation and GIS tools. Chem. Eng. Res. Des. 90, 2209–2222. Marseguerra, M., Zio, E., Podofillini, L., 2004. Optimal reliability/availability of uncertain systems via multi-objective genetic algorithms. IEEE Trans. Reliab. 53, 424–434. Rocha, D.M., Cardoso, C.D.O., Borges, R.G., Baioco, J.S., Coutinho, D.D.C.E.S., Albrecht, C.H., Jacob, B.P., 2015. Optimization of submarine pipeline routes considering slope stability. pp. 761-776. Rose, D., Schmidt, M., Steinbach, M.C., Willert, B.M., 2016. Computational optimization of gas compressor stations: minlp models versus continuous reformulations. Math. Methods Oper. Res. 83, 409–444. Rosenthal, A., 2010. Dynamic programming is optimal for nonserial optimization problems. SIAM J. Comput. 11, 47–59. Rothfarb, B., Frank, H., Rosenbaum, D.M., Steiglitz, K., Kleitman, D.J., 1970. Optimal design of offshore natural-gas pipeline systems. Oper. Res. 18, 992–1020. Ruan, Y., Liu, Q., Zhou, W., Batty, B., Gao, W., Ren, J., Watanabe, T., 2009. A procedure to design the mainline system in natural gas networks. Appl. Math. Model 33, 3040–3051. Sahebi, H., Nickel, S., 2014. Offshore oil network design with transportation alternatives. Eur. J. Ind. Eng. 8, 739. Schwarz, L., Robl, K., Wakolbinger, W., Mühling, H., Zaradkiewicz, P., 2015. GIS Based, Heuristic Approach for Pipeline Route Corridor Selection. Springer International Publishing. Trangenstein, J.A., Bell, J.B., 1989. Mathematical structure of the black-oil model for petroleum reservoir simulation. SIAM J. Appl. Math. 49, 749–783. Tsibulnikova, M.R., Kupriyanova, O.S., Strelnikova, A.B., 2015. Economic assessment of environmental impact in the course of oil field development and production. In: IOP Conference. p. 012076. Vieira, I.N., Albrecht, C.H., Lima, B.S.L.P.D., Jacob, B.P., Rocha, D.M., Oliveiracardoso, C.D., 2010. Towards a computational tool for the synthesis and optimization of submarine pipeline routes. Wang, Y., Duan, M., Xu, M., Wang, D., Feng, W., 2012. A mathematical model for subsea wells partition in the layout of cluster manifolds. Appl. Ocean Res. 36, 26–35. Wang, Y., Zhang, X., Zhao, Y., Chen, H., Duan, M., Estefen, S.F., 2017. Perturbation analysis for upheaval buckling of imperfect buried pipelines based on nonlinear pipesoil interaction. Ocean Eng., 92–100. Wu, Y., Lai, K.K., Liu, Y., 2007. Deterministic global optimization approach to steadystate distribution gas pipeline networks. Optim. Eng. 8, 259–275. Zhang, H., Liang, Y., Wu, M., Qian, C., Li, K., Yan, Y., 2015. Study on the optimal topological structure of the producing pipeline network system of CBM fields. In: International Petroleum Technology Conference. Doha, Qatar.
5. Conclusions This paper proposes an MILP method to figure out the globally optimal network topology, location of center platform, pressure increment and dehydrating facilities and diameter and route of pipeline with given wellheads locations and submarine terrain. This paper considers the construction costs of platforms and pipes and establishes an MILP model with the objective function to minimize total investment and the constraints of submarine terrain and production process. And the model is solved by GUROBI. Finally, this paper takes offshore production system with half-offshore and half-continent mode and offshore mode for instances, and works out the optimally global distribution of gathering pipeline network. The proposed methods can lower the total construction cost when compared with that of the previous methods, and it testifies the accuracy of the proposed model. This model can provide theoretical and technical support for further offshore oilfield gathering system optimization. References And, R.R.I., Grossmann, I.E., And, S.V., Cullick, A.S., 1998. Optimal planning and scheduling of offshore oil field infrastructure investment and operations. Ind. Eng. Chem. Res. 37, 1380–1397. Baumrucker, B.T., Biegler, L.T., 2010. MPEC strategies for cost optimization of pipeline operations. Comput. Chem. Eng. 34, 900–913. Brimberg, J., Hansen, P., Lin, K.W., Mladenovic, N., Breton, M., 2003. An oil pipeline design problem. Oper. Res. 51, 228–239. Carvalho, M.C.A., Pinto, J.M., 2006. An MILP model and solution technique for the planning of infrastructure in offshore oilfields. J. Pet. Sci. Eng. 51, 97–110. Dan, A., Williams, M., 2015. GIS-based optimal route selection for oil and gas pipelines in Uganda. Adv. Comput. Sci. 4, 93–104. Dey, P.K., Ogunlana, S.O., Naksuksakul, S., 2004. Risk‐based maintenance model for offshore oil and gas pipelines: a case study. J. Qual. Maint. Eng. 10, 169–183. Dolan, W.B., Cummings, P.T., Levan, M.D., 1989. Process optimization via simulated annealing: application to network design. Aiche J. 35, 725–736. Duan, Z., Liao, Q., Wu, M., Zhang, H., Liang, Y., 2016. Optimization of pipeline network structure of cbm fields considering three-dimensional geographical factors. In: Proceedings of the 11th International Pipeline Conference. Calgary, Alberta, Canada. Gramling, R., Freudenburg, W.R., 2006. Attitudes toward offshore oil development: a summary of current evidence. Ocean Coast. Manag. 49, 442–461. Gupta, V., Grossmann, I.E., 2012. An efficient multiperiod MINLP model for optimal planning of offshore oil and gas field infrastructure. Ind. Eng. Chem. Res. 51, 6823–6840. Haneberg, W.C., 2015. Evaluating the Effects of Input Cost Surface Uncertainty on DeepWater Petroleum Pipeline Route Optimization. Springer International Publishing. Jr, M.H.A.D.L., Baioco, J.S., Albrecht, C.H., Lima, B.S.L.P.D., Jacob, B.P., Rocha, D.M., Cardoso, C.D.O., 2011. Synthesis and optimization of submarine pipeline routes considering on-bottom stability criteria. In: ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. pp. 307-318. Kabirian, A., Hemmati, M.R., 2007. A strategic planning model for natural gas transmission networks. Energy Policy 35, 5656–5670. Kawsar, M.R.U., Youssef, S.A., Faisal, M., Kumar, A., Seo, J.K., Paik, J.K., 2015.
34
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
An MILP method for optimal offshore oilfield gathering system a
a,⁎
a
b
MARK
a
Haoran Zhang , Yongtu Liang , Jing Ma , Chen Qian , Xiaohan Yan
a National Engineering Laboratory for Pipeline Safety/Beijing Key Laboratory of Urban oil and Gas Distribution Technology, China University of PetroleumBeijing, Fuxue Road No.18, Changping District, Beijing 102249, PR China b University of Calgary, 2500 University Drive, NW, Calgary, Alberta, Canada T2N 1N4
A R T I C L E I N F O
A BS T RAC T
Keywords: Offshore oilfield Gathering pipeline system Optimization Pipeline network topology
Offshore oilfield gathering system plays a key role in oilfield exploration and production process, the rational construction of the gathering system is directly related to the efficiency and profit of the offshore oilfield production. Thus, optimization of the whole gathering system is the key to lower the offshore oilfield production cost, and it also has been one of the major challenges in offshore oilfield production. Many researches have been done on the optimization but pipeline network distribution, treating technical and integrated optimization still remained unsolved. This paper focuses on the common offshore oilfield gathering network construction, taking gathering radius, economic flowrate, terrain obstacles and production technic into consideration, building a mixed integer linear programming (MILP) model, figuring out the globally optimal connection topology, location of center platforms, pressure increment and dehydrating facilities and major parameters of each pipeline, and contributing to further optimal offshore oilfield engineering mode. Last, this paper takes two typical real cases, namely half-offshore and half-continent mode and offshore mode, to test the accuracy of the proposed model. The optimal results indicate the proposed method can lower the general investment and testify the liability and applicability of it.
1. Introduction 1.1. Background Petroleum industry plays a vital role in the modern global economy, owing to the fact that it is the largest source of energy in the world (Sahebi and Nickel, 2014). Across the intervening years, offshore exploration and production have spread around the world, taking place off the coasts of Africa, Asia, Central and South America, and Europe (Gramling and Freudenburg, 2006). Offshore gathering pipeline system collects, disposes and transfers the produced liquid and plays a key role in the whole offshore production system (Kawsar et al., 2015; Wang et al., 2017). The construction of offshore gathering system costs a huge part of the oilfield production investment (Kearney, 2010; Tsibulnikova et al., 2015). The rational construction of it is directly related to the efficiency and profit of the offshore oilfield production. Thus, the optimization of the whole gathering system is the key to lower the offshore oilfield production cost, and it is also one of the major challenges in offshore oilfield production (Liu et al., 2015). Offshore oilfield gathering pipeline system optimization contains optimal well groups division, geometric center of points set location (Li et al., 2011), minimum spanning tree of graph theory (Rothfarb et al.,
⁎
Corresponding author. E-mail address: [email protected] (Y. Liang).
http://dx.doi.org/10.1016/j.oceaneng.2017.06.011 Received 3 November 2016; Received in revised form 27 May 2017; Accepted 5 June 2017 0029-8018/ © 2017 Elsevier Ltd. All rights reserved.
1970), shortest route (Knoope et al., 2014; Marcoulaki et al., 2012) and many other sub questions. Most of the sub questions are typical nondeterministic polynomial complete (NPC) models. Usually these sub questions are coupled, and considering the direction of pipeline (Dan and Williams, 2015; Schwarz et al., 2015), topology, submarine geomorphology and obstacles (Haneberg, 2015; Rocha et al., 2015) and production technical, thus the offshore oilfield gathering pipeline optimization can be very complex. Moreover, the current models and methods are unable to solve complex connections and general and globally optimal results. This paper focuses on the common offshore oilfield gathering network construction, taking gathering radius, submarine geomorphology and obstacles, and production technic into consideration, building an MILP model, figuring out the global connection topology, center platform location, pressure increment and dehydrating facilities and major parameters of each pipeline, and contributing to further optimal offshore oilfield engineering mode. 1.2. Related work Since the offshore oil field gathering system is complex, many scholars have carried out researches on different aspects of this issue. In the work of And et al. (1998), he employed a general objective
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Nomenclature
Rmax RP max
Acronyms
Discrete parameters
NPC problem Non-deterministic Polynomial Complete problem. NPV Net Present Value. MIP Mixed Integer Programming. MILP Mixed-Integer Linear Programming. MINLP Mixed-Integer Non-Linear Programming. GDP Gross Domestic Product.
FIPx, y FDDx, y FWPx, y
Sets and indices
FPFx, y, r
(x, y), (rxx, y, r , ryx, y, r ) ∈ XY Set of gird coordinate. r , rrr ∈ R Set of connection direction. d∈D Set of pipe diameter. v∈V Set of flowrate classes.
CPFQ CPv CPPQ CBCx, y CDd LDx, y, r
M γ Q PV max v Q PV min v Q DF max d Q DF min d Q WPx, y
Platform construction binary variable. FIPx, y = 1 if (x, y) is suitable for constructing a platform, or else, FIPx, y = 0 . Onshore terminal binary variable. FDDx, y = 1 if (x, y) is onshore terminal, or else, FDDx, y = 0 . Wellhead location binary variables. FWPx, y = 1 if (x, y) is wellhead, or else, FWPx, y = 0 . Pipeline installation condition binary variable. FPFx, y, r = 1 if pipeline could start from (x, y) to the adjacent node along direction r, or else, FPFx, y, r = 0 .
Continuous variables
Q Dx, y, r Q Px, y Q PFx, y Q DDx, y Q PPx, y Hx, y
Continuous parameters
CFx, y CPFv
wellhead. Maximum gathering radius. Maximum gathering radius increment powered by pumps.
Platform construction cost at (x, y). Separating facilities cost when separating liquid in volume flowrate class v . Dehydrating cost for a volume crude oil. Pressure increment facilities cost when transferring liquid in volume flowrate class v . Pressure increment cost for a volume crude oil. Center platform construction cost at (x, y). Construction unit price of pipeline with diameter d . Connecting distance from (x, y) to the adjacent node along direction r . A maximum value Dehydrating efficiency Upper bound of flowrate class v . Lower bound of flowrate class v . Upper bound of economic flowrate of pipeline with diameter d . Lower bound of economic flowrate of pipeline with diameter d . Output of wellhead (x, y). Q WPx, y = 0 if (x, y) is not a
Flowrate from (x, y) to the adjacent node along direction r . Platform receiving flowrate at (x, y). Free water volume separated at (x, y). Final receiving flowrate at (x, y). Flowrate at pressure increment facility (x, y). Equivalent connection length at (x, y).
Binary variables
BFx, y BCx, y BPFx, y, v
BPx, y, v
BDx, y, r , d
Platform construction binary variable. BFx, y = 1 if platform is constructed at (x, y), or else, BFx, y = 0 . Center platform construction binary variable. BCx, y = 1 if platform is constructed at (x, y), or else, BCx, y = 0 . Dehydrating facility construction binary variable. BPFx, y, v = 1 if dehydrating facility is constructed at (x, y), or else, BPFx, y, v = 0 . Pressure increment facility construction binary variable. BPx, y, v = 1 if pressure increment facility is constructed at (x, y), or else, BPx, y, v = 0 . BDx, y, r , d = 1 if pipeline with diameter d could start from (x, y) to adjacent node along direction r , or else, BDx, y, r , d = 0 .
considered the optimal layout problem for a pipeline of given length in the presence of uncertainties in the failure rates of its constituent parts (i.e. pipes and joints). Wu et al. (2007) established a mathematical optimization model for the problem of minimizing the cost of pipelines incurred by driving the gas in a distributed non-linear network, based on distribution gas pipeline networks which had a steady demand. The decision variables included the selection of the pipes’ diameter, pressure drops at each node of the network, and mass flow rate at each pipeline leg. Ruan et al. (2009) presented a model that minimized the total pipeline and compressors investment cost for onshore natural gas transmission pipelines, and proposed a rank-optimization method to solve the model. Marcoulaki et al. (2012) established a nonlinear programming model for pipeline route optimization, which considered process constraints and was solved by stochastic optimization method. Zhang et al. (2015) developed several programming models respectively for multiple connection modes of onshore gathering networks and an improved genetic algorithm was used to figure out the model. Then Duan et al. (2016) proposed a two-stages method based on Zhang et al. (2015), considering geographic factors. Despite the comprehensive coverage of network connection modes, those methods are hard to ensure the result calculated by intelligence algorithms has global optimality. Yet it is difficult to guarantee the optimality of the results obtained by intelligent algorithms as the model scale increased (Jr
function of MILP model that optimized a selected economic indicator (e.g., net present value) and incorporated the nonlinear reservoir performance, surface pressure constraints, and drilling rig resource constraints. Carvalho and Pinto (2006) proposed a mixed integer programming (MIP) with the discrete and continuous decisions to maximize the net present value and took the pressure of each reservoir. Gupta and Grossmann (2012) solved the offshore oilfield development problem based on the multi-period non-convex mixed-integer nonlinear programming (MINLP) model aiming at obtaining the maximizing total net present value (NPV) for long-term planning horizon. As for the topological optimization of natural gas transmission networks, Kabirian and Hemmati (2007) proposed an MINLP model combining installation and operating costs, to develop optimal network structures by selecting the type and location of pipeline and compressor stations. Sahebi and Nickel (2014) came up with a mixed integer model to design the oilfield development and plan crude oil transportation problems. For the nonconvex mixed-integer nonlinear optimization problems, Rose et al. (2016) established MINLP model for operating a single station and discussed several continuous reformulations of the problem. However, researchers mentioned above had not considered geomorphology or process constraints. Intelligent algorithms have been applied to solve complex topology structures of oil and gas gathering networks. Marseguerra et al. (2004)
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center platform location, pressure increment and dehydrating facilities location, parameters and route of pipes and compares the optimal result with that of current algorithms.
et al., 2011; Vieira et al., 2010). Furthermore, intelligent algorithms could easily converge to the locally optimal solution as a result of the strong randomness, thus the calculation results need to be further discussed. Some scholars have tried to deal with network structure topology optimization by heuristic algorithms. Rothfarb et al. (1970) put forward three fundamental issues for topology optimization of offshore natural gas pipeline networks: (1) selection of pipe diameters in a specified pipeline network to minimize the sum of investment and operation costs; (2) selection of minimum-cost network structures, given gas-field locations and flow requirements; (3) optimal expansion of existing pipeline networks to include newly discovered gas fields. And techniques were attempted to put into practice, which were incorporated procedures for globally optimizing pipeline diameters for fixed tree structures and heuristic procedures for generating lowcost structures. But geomorphology constraints were not taken into consideration. Dolan et al. (1989) combined the approach of Rothfarb et al. (1970) with simulated annealing and came up with a different approach to the pipeline network design problem. Recently，Rosenthal (2010) studied the solution of the pipe diameter problem by non-serial dynamic programming. Baumrucker and Biegler (2010) developed a mathematical program with equilibrium constraints (MPECs) approach for efficient operation of gas pipelines. Wang et al. (2012) established a mathematical model for topology optimization of the submarine cluster structures and proposed a heuristic algorithm based on the hyperlink matrix. Whereas factors such as terrain and obstacles were not taken into account, and the proposed algorithm was confined to the specific structure optimization of pipe networks. Brimberg et al. (2003) built up a mixed integer programming model (MILP) for the optimization of nearshore pipeline network arrangement and pipeline type. And the tabu search and variable neighborhood search were coupled together to solve the model. Dey et al. (2004) developed a risk-based maintenance model using a combined multiple-criteria decision-making and weight method for offshore oil and gas pipelines. Lucena et al. (2014) dealt with the route optimization of subsea gathering pipelines by establishing a mathematical programming model, considering the constraints of subsea obstacles. The evolutionary algorithm was determined to solve the model. Since only the line selection between two points could be carried out by the model, it failed to be directly applied for global optimization of pipeline networks. However, the heuristic algorithms mentioned above have poor universal application for it only aims to the specific problems subjected to the model constraints. Thus, current models and algorithms cannot solve the complex connection and integral solution problem. This paper builds an MILP model with submarine obstacles and production technic as constraints for common offshore oilfield pipeline network connection, and figures out the globally optimal topology,
2. Methodology 2.1. Problem description Offshore oilfield production usually sets wellhead platforms or center platforms at the wellheads. In this paper, the wellhead platforms can be defined as the satellite platforms which connect to the center platform by stellated connection mode and there is no connection among wellhead platforms. Since the deck of the wellhead platform is small, the pressure increment and processing facilities are not allowed to be installed. The center platforms can be connected to each other to receive the produced liquid from wellhead platforms. Contrary to the wellhead platform, the deck of the center platform is larger, which can place the pressure increment and processing facilities. Platforms are connected by submarine pipelines. When installing the submarine pipes, designers should consider the submarine terrain and obstacles, install on ideal geological conditions with smooth slope and avoid trench and faults. Meanwhile, if two destinations are away from each other, pressure increment facilities should be taken into consideration. If the produced liquid at wellheads contains a large amount of water, dehydrating facilities should be taken into consideration as well. Offshore oilfield engineering modes include half-offshore and halfcontinent mode and offshore mode, as shown in Fig. 1. In the first mode, offshore produced liquid will first be separated into oil and water and then transferred to onshore terminal for further process. Installing submarine pipes cost a lot, thus this mode can only be applied to a short distance offshore production block. Accordingly, offshore production mode can be applied to a long distance offshore oilfield. In this mode, FPSO is used for oil processing and storage instead of onshore terminal. The essence to optimize offshore oilfield gathering system is the selection and optimization of wellhead position, platform location, network distribution, pipe diameter and length, pressure increment and dehydrating facilities location. The model adopts the discrete mesh division by which the study area is divided into a number of sub-squares. The 16 node-type connection structure is applied to build up the corresponding constraint equations, function objective and the programming model for each sub-square. As shown in Fig. 2, R is the number set of connection direction between node and the subscript is represented by r while rrr as the opposite direction of r . XY is the coordination set of all the mesh nodes in study area. Supposing node (x′, y′) as the terminal of node (x, y) going through a distance along the direction r , define x′ = rxx, y, r and y′ = ryx, y, r . Similarly, node (rxx, y, rrr , ryx, y, rrr ) is obtained by node (x, y) along the opposite direction of r .
Fig. 1. Offshore oilfield gathering system. (a) half-offshore and half-continent mode (b) offshore mode.
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2.3. MILP model Based on MILP model structures, an optimization model for offshore oilfield gathering system is proposed in this paper, which aims to work out a offshore oilfield gathering system with the least construction cost under the premise of production and hydraulic constraints. Combined with specific actual data, the optimization issue of offshore oilfield gathering system can be transformed into an MILP mathematical model, and then solved by mature MILP solver. The optimal construction scheme of offshore oilfield gathering system can be obtained. To intuitively show the proposed model, the following compact form is presented. The detailed content will be elaborated in Section 3.
min F ( pi , pl , pr , Qn ) pi, pl, pr , Qn
s.t.φ ( pl , pr , Qn ) ≤ 0 ψ ( pi , Qp ) ≤ 0 ϕ ( pi , Qp , Qn ) = 0 ξ ( pi ) ≤ 0
(1)
where: pi represents design variables of submarine pipelines. pl represents design variables of platforms. pr represents design variables of processing facilities. Qn represents variables of node flowrate. Qp represents variables of pipeline flowrate. F represents objective function. φ represents universal constraints of platform construction. ψ represents universal constraints of pipeline flowrate. ϕ represents universal constraints of flowrate balance. ξ represents universal constraints of pipeline construction. As seen from Eq. (1), the objective function of the optimization model of offshore oilfield gathering system is associated with pipelines, platforms, processing facilities, and processing capacity of the system. There are four types of constraints in the optimization model. The first type is constraints of platform construction φ , which mainly describe the construction location of platforms and the specification of processing facilities. Those constraints involve pl , pr and Qn . The second type is constraints of pipeline flowrate ψ , which mainly describe the relationship between size of pipeline and pipeline flowrate. Those constraints are related with pi and Qp . The third type is constraints of flowrate balance ϕ , which mainly describe the flowrate of each node with specific pipeline connection structures and the relationship between each pipeline flowrate. The last type is constraints of pipeline construction ξ , which mainly describe the constraints on pipeline connection structure due to gathering radius limit and are related with pi .
Fig. 2. Mesh division and direction.
2.2. Model requirements The model is formulated as MILP and the optimization is executed using GUROBI. A detailed offshore oilfield gathering pipeline system construction scheme can be obtained by solving the model. Given: 1. well group information: well group location, well group output, water cut of produced liquid 2. obstacle information 3. gathering radius 4. construction unit price: pipe unit price (of different diameters), platform construction unit price, dehydrating facilities unit price Determine: 5. pipeline connection mode 6. pipeline diameter based on economic flowrate 7. pipeline flow direction 8. center platform location Objective: The objective is to minimize the total costs, including pipeline costs, platform and affiliated facilities construction costs, pressure increment and dehydrating facilities costs and the cost of pressure increment and dehydrating process, and to work out a detailed offshore oilfield gathering pipeline system construction scheme under various operational and technical constraints. In order to solve the model more efficiently, assuming: 9. To make sure the designed gathering system can work safely, this paper takes gathering radius as the model constraint. If the gathering and transferring distance is less than the gathering radius, this paper assumes the whole system meets the hydraulic and thermal requirements. 10. During the submarine pipeline designing process, the first step is primarily selecting several pipe diameters based on economic flowrates, then taking flow, mechanic and transfer conditions into consideration and determining the exact diameter. This paper selects the final diameter based on economic flowrates. The selected diameter should be further testified under the in sit condition. 11. This paper assumes the pressure increment facilities have enough power to transfer the oil till the terminal, and the produced oil just can go through only one dehydrating and pressure incrementing process.
3. Mathematical formulations 3.1. Objective function The objective function is to work out the offshore oilfield construction scheme with lowest cost under each given constraint. Total costs include platform and its affiliated facilities construction costs and pipeline construction costs. Platforms and their affiliated facilities construction costs include platform construction costs, dehydrating and pressure increment facilities costs. The latter costs depend on the oil volume they processed.
f1 =
∑ ∑ x
y
⎛ ⎜⎜CFx, y BFx, y + ⎝
∑
CPFv BPFx, y, v + CPFQ Q Px, y
v
⎞ + ∑ CPv BPx, y, v + CPPQ Q PPx, y + CBCx, y BCx, y⎟⎟ ⎠ v (x, y) ∈ XY , v ∈ V
(2)
Pipeline construction costs depend on pipeline diameter and length. 28
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f2 =
Boosted flowrate equals to platform receiving flowrate if there are no process facilities.
∑ ∑ ∑ ∑ CDd LDx,y,r BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D x
y
r
(3)
d
⎛ ⎜⎜1 − ⎝
3.2. Constraints of platform construction
∑ BPFx,y,v M + QPPx,y ≤ QPx,y (x, y) ∈ XY , v ∈ V v
(18) Boosted flowrate equals to the platform receiving flowrate minus dehydrating flowrate if there is a process facility.
There must be a platform at the well head.
⎛ ⎜⎜1 − ⎝
(5)
The receiving flowrate must be zero if there is no platform.
BFx, y M ≥ Q Px, y (x, y) ∈ XY
v
⎛ ⎞ ⎜⎜∑ BPx, y, v − 1⎟⎟ M − ⎝ v ⎠
(4)
FWPx, y ≤ BFx, y (x, y) ∈ XY
⎠
v
(17)
The platform construction binary variable must equal to 0 if this spot is not suitable for setting a platform. FIPx, y denotes the suitability of setting a platform and FIPx, y = 1 if this spot is suitable for setting a platform. BFx, y denotes platform construction binary variable. If this spot is suitable for setting a platform, then BFx, y = 1, or else, BFx, y = 0 .
BFx, y ≤ FIPx, y (x, y) ∈ XY
⎞
∑ BPx,y,v⎟⎟ M + ∑ BPFx,y,v M + QPPx,y ≥ QPx,y (x, y) ∈ XY , v ∈ V
⎞
⎛
⎠
⎝
⎞
∑ BPx,y,v⎟⎟ M + ⎜⎜1 − ∑ BPFx,y,v⎟⎟ M + QPPx,y ≥ QPx,y − QPFx,y (x, y) v
⎠
v
(19)
∈ XY , v ∈ V
(6)
⎛ ⎞ ⎛ ⎞ ⎜⎜∑ BPx, y, v − 1⎟⎟ M + ⎜⎜∑ BPFx, y, v − 1⎟⎟ M + Q PPx, y ≤ Q Px, y − Q PFx, y (x, y) ⎝ v ⎠ ⎝ v ⎠
The receiving flowrate equals to the sum of produced flowrates at each node and the influx flowrate from other nodes.
∑ QDrxx,y,r,ryx,y,r ,rrr + (1 − BFx,y) M + Q WPx,y ≥ QPx,y (x, y), (rxx,y,r , ryx,y,r )
(20)
∈ XY , v ∈ V
r
The constraints of pressure increment facilities are the same as those of dehydrating facilities.
(7)
∈ XY , r , rrr ∈ R
∑ QDrxx,y,r,ryx,y,r ,rrr + (BFx,y − 1) M + Q WPx,y ≤ QPx,y (x, y), (rxx,y,r , ryx,y,r )
(1 − BPx, y, v ) M + Q PV max v ≥ Q PPx, y (x, y) ∈ XY , v ∈ V
(21)
(BPx, y, v − 1) M + Q PV min v ≤ Q PPx, y (x, y) ∈ XY , v ∈ V
(22)
r
∈ XY , r , rrr ∈ R
(8)
Dehydrating and pressure increment facilities must be installed on a platform.
∑ BPFx,y,v ≤ BFx,y (x, y) ∈ XY , v ∈ V v
3.3. Constraints of pipeline and node flowrate Transferring flowrate must equal to zero if there are no pipes between two spots.
(9)
Dehydrating flowrate must equal to zero if there are no dehydrating facilities at this spot
∑ BPFx,y,v M ≥ QPFx,y (x, y) ∈ XY , v ∈ V v
∑ BDx,y,r,d M ≥ QDx,y,r (x, y) ∈ XY , r ∈ R, d ∈ D
There must be no pipes in between if the transferring flowrate equals to zero.
(10)
Dehydrating flowrate equals to processing flowrate times dehydrating efficiency.
⎛ ⎜⎜1 − ⎝
⎞ ∑ BPFx,y,v⎟⎟ M + QPx,y γ ≥ QPFx,y (x, y) ∈ XY , v ∈ V ⎠ v
⎛ ⎞ ⎜⎜∑ BPFx, y, v − 1⎟⎟ M + Q Px, y γ ≤ Q PFx, y (x , y) ∈ XY , v ∈ V ⎝ v ⎠
Q Dx, y, r M ≥
∑ BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D
Determine transferring flowrate classes.
(11)
(12)
(1 − BPFx, y, v ) M + Q PV max v ≥ Q Px, y (x, y) ∈ XY , v ∈ V
(13)
(BPFx, y, v − 1) M + Q PV min v ≤ Q Px, y (x, y) ∈ XY , v ∈ V
(14)
(1 − BDx, y, r , d ) M + Q DF max d ≥ Q Dx, y, r (x, y) ∈ XY , r ∈ R, d ∈ D
(25)
(BDx, y, r , d − 1) M + Q DF min d ≤ Q Dx, y, r (x, y) ∈ XY , r ∈ R, d ∈ D
(26)
Final receiving flowrate of any node except onshore terminal nodes must equal to zero.
Q DDx, y ≤ FDDx, y M
(x, y) ∈ XY
Q WPx, y +
∑ QDrxx,y,r,ryx,y,r ,rrr = QDDx,y + ∑ QDx,y,r + QPFx,y (x, y), r
r
(rxx, y, r , ryx, y, r ) ∈ XY , r , rrr ∈ R
v
(28)
The sum of transferring flowrates at onshore terminal nodes equals to the sum of all production flowrates at wellheads minus the free water flowrates at each dehydrating node.
(15)
Boosted flowrate must equal to zero if there are no pressure increment facilities.
∑ BPx,y,v M ≥ QPPx,y (x, y) ∈ XY , v ∈ V
(27)
The sum of production flowrates at wellheads and influx flowrates from adjacent nodes equal to the sum of final receiving flowrate, the out flux flowrate of this node and the free water flowrate after dehydrating process.
Pressure increment facilities must be installed on a platform.
v
(24)
d
There are different kinds of classes for dehydrating facilities, and in virtue of their flowrate limits, the corresponding facilities should be determined based on the real flowrates. If the platform has to construct dehydrating facility (When ∑v BPFx, y, v = 1) and the receiving flowrate Q Px, y is in class v′ (When ∑v BPFx, y, v = 1 and Q PV min v ′ ≤ Q Px, y ≤ Q PV max v ′), the processing capacity class of dehydrating facility must be equal to v′(BPFx, y, v ′ = 1).
∑ BPx,y,v ≤ BFx,y (x, y) ∈ XY , v ∈ V
(23)
d
(1 − FDDx, y ) M +
∑ ∑ Q WPx,y − ∑ ∑ QPFx,y ≥ ∑ QDrxx,y,r,ryx,y,r ,rrr (x, y), x
(16)
y
x
y
r
(rxx, y, r , ryx, y, r ) ∈ XY , r , rrr ∈ R 29
(29)
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(FDDx, y − 1) M +
∑ ∑ Q WPx,y − ∑ ∑ QPFx,y ≤ ∑ QDrxx,y,r,ryx,y,r ,rrr (x, y), x
y
x
y
increase the transferring distance of the gathering system. Equivalent largest connecting distance has a maximum value based on the efficacious workaround of pumps.
r
(rxx, y, r , ryx, y, r ) ∈ XY , r , rrr ∈ R
(30)
−RP max ≤ Hx, y
One node can have up to one flow direction and one route connected with the adjacent node. Onshore terminal nodes must have no further connection.
1 − FDDx, y ≥
∑ ∑ BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D r
d
(x, y) ∈ XY
(41)
Each route can only have one pipe.
∑ BDx,y,r,d + ∑ BDrxx,y,r,ryx,y,r ,rrr,d ≤ 1(x, y), (rxx,y,r , ryx,y,r ) ∈ XY , r , r d
d
(31)
rr ∈ R, d ∈ D
(42)
Wellhead nodes must have a further connection.
FWPx, y ≤
∑ ∑ BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D r
d
4. Results and discussion
(32)
A platform has a maximum amount of further connecting pipes.
(1 − BFx, y ) M + NP ≥
The proposed method can be applied to the optimization of offshore oilfield gathering system for half-offshore and half-continent mode and offshore mode. This paper testifies the applicability and accuracy of the method by using the following two cases. MATLAB R2014a is taken as programming environment and GUROBI Optimizer is chosen to solve the proposed MILP model. GUROBI Optimizer is a state-of-the-art solver for mathematical programming. The solvers in GUROBI Optimizer are designed from the ground up to exploit modern architectures and multi-core processors, using the most advanced implementations of the latest algorithms. There is the built-in improved branch and bound algorithm solving MILP models, which is a search algorithm for globally optimal solution. Thus, the globally optimal design solution of offshore oilfield gathering system can be obtained by the proposed model and GUROBI Optimizer.
∑ ∑ BDrxx,y,r,ryx,y,r ,rrr,d (x, y), (rxx,y,r , ryx,y,r ) ∈ XY , r r
d
(33)
, rrr ∈ R, d ∈ D
One node can only have up to one other node transferring liquid if this node is neither wellheads nor onshore terminal.
BFx, y M + FDDx, y M + 1 ≥
∑ ∑ BDrxx,y,r,ryx,y,r ,rrr,d (x, y), (rxx,y,r , ryx,y,r ) r
d
∈ XY , r , rrr ∈ R, d ∈ D
(34)
Connection binary variable must equal to zero if this spot is unsuitable for constructing pipes.
FPFx, y, r ≥
∑ BDx,y,r,d (x, y) ∈ XY , r ∈ R, d ∈ D d
(35) 4.1. Example 1
3.4. Constraints of pipeline construction
Taking a offshore 15 km × 15 km block for instance. Given 8 well groups, each has certain amount of wellheads. Offshore drilling and production are usually based on platform, all wellheads are collected to the platform as the center. As shown in Fig. 3, the grey area indicates the obstacles and is unsuitable for installing pipeline and stations. The black dots in the figure indicate the well group locations, and output of well group is shown in Table 1. The red square indicates the onshore terminal, and all produced liquid must be transferred to the onshore terminal. Costs of wellhead and center platforms are shown in Table 2. Only the center platform can receive oil from other platforms, and there must be a platform at wellhead. Different pipeline diameters and
Equivalent largest connecting distance of one node equals to zero if this node has no connection with other nodes.
Hx, y ≤
∑ ∑ BDx,y,r,d M + ∑ ∑ BDrxx,y,r,ryx,y,r ,rrr,d M (x, y) r
d
r
d
(36)
∈ XY , r ∈ R, d ∈ D
Equivalent largest connecting distance of one node equals to the sum of equivalent largest connecting distance of the previous node and the connecting distance if there are no pressure increment facilities at this node.
Hx, y ≤ Hrxx, y, r , ryx, y, r + LDrxx, y, r , ryx, y, r , rrr +
∑ BPx,y,v M v
⎛ + ⎜⎜1 − ⎝
⎞ ∑ BDrxx,y,r,ryx,y,r ,rrr,d ⎟⎟ M ⎠ d
Hx, y ≥ Hrxx, y, r , ryx, y, r + LDrxx, y, r , ryx, y, r , rrr −
(37)
∑ BPx,y,v M v
⎛ ⎞ + ⎜⎜∑ BDrxx, y, r , ryx, y, r , rrr , d − 1⎟⎟ M ⎝ d ⎠
(38)
(x, y), (rxx, y, r , ryx, y, r ) ∈ XY , r , rrr ∈ R, d ∈ D Equivalent largest connecting distance of a wellhead node must be a positive value if there are no pressure increment facilities attached.
Hx, y + (1 − FWPx, y ) M ≥ −∑ BPx, y, v M v
(x, y) ∈ XY (39)
Equivalent largest connecting distance of any node must be less than the largest gathering radius.
Hx, y ≤ Rmax
(x, y) ∈ XY
(40)
Equivalent largest connecting distance of one node could be less if there are pressure increment facilities at this node, which could
Fig. 3. Oilfield wellhead and onshore terminal position of example 1.
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Table 1 Well group output of example 1.
Table 4 Pressure increment and dehydrating facilities costs.
No.
Output (m3/d)
No.
Output (m3/d)
processing capacity class
Ⅰ
Ⅱ
Ⅲ
Ⅳ
Ⅴ
1 2 3 4
2480 1390 2800 3680
5 6 7 8
2340 3180 2460 2310
Upper flowrate limit of pressure increment facilities (m3/d) Lower flowrate limit of pressure increment facilities (m3/d) Pressure increment facilities cost (million dollar) Upper flowrate limit of dehydrating facilities (m3/d) Lower flowrate limit of dehydrating facilities (m3/d) Dehydrating facilities costs (million dollar)
14,000
18,000
22,000
24,000
28,000
10,000
14,000
18,000
22,000
24,000
14.57
16.03
17.48
18.94
21.86
14,000
18,000
22,000
24,000
28,000
10,000
14,000
18,000
22,000
24,000
29.14
30.60
32.05
33.51
36.43
Table 2 Platform costs. Category
Cost (thousand dollar)
Infrastructure cost Unit price with depth Center platform
48,663.8 1457 80,135
Table 5 The property of the produced liquid.
the corresponding economic flowrate classes are shown in Table 3. Pressure increment and dehydrating facilities can only be installed on the center platform, and there must be supporting facilities such as increased floor space and electricity. The corresponding costs are shown in Table 4. The processing flowrate class represents the facility processing capacity which keeps proportional to the flowrate. There are five different kinds of classes for pressure increment and dehydrating facilities, and in virtue of their flowrate limits, the corresponding facilities should be determined based on the real flowrates, as shown in constraints 13,14,21,22. The property of the produced liquid is shown in Table 5. The results are shown in Fig. 4. The yellow dots and green dots respectively indicate the locations of satellite platforms and center platforms. And the blue dots represent center platforms equipped with pressure increment and dehydrating facilities after optimization on the original center platforms. The pipeline network after optimization meets all constraints requirements. The pipe length of each pipeline diameter is shown in Table 6. The implementation result shows that the center platform should be constructed at dot 8 and the pressure increment facilities (classⅠ) and dehydrating facilities (classⅢ) are needed. The main reason is that the distance between the dot 8 and the terminal is so long that the wellhead pressure is not enough, thereby needing to build the pressure increment facilities. Meanwhile, it is not economic to transport the crude oil with free water to the terminal on account of the high water content in the produced liquid. Therefore, the dehydrating facilities are necessary for the free water separation. In the light of the existing topology of the pipeline network, PIPESIM was used for hydrothermal check. The modelling interface of PIPESIM is shown in Fig. 5. PIPESIM is a set of simulation calculator of steady-state multiphase flow developed by
Example
Free water ratio/%
Density / (kg m−3)
Viscosity / (mPa s)
Initial boiling point /℃
Wax content / %
Example 1 Example 2
46 53
938.2 937.4
184.1 174.5
148 142
7.42 9.38
Schlumberger. The built-in black oil model (Trangenstein and Bell, 1989) of the software was applied to simulation of oil liquid and the built-in Beggs-Brill equation to calculation of pressure drop. The dot pressure is shown in Fig. 6, which indicated the result can satisfy the requirement. 4.2. Example 2 Taking a offshore 15 km × 15 km block for instance. Given the location and output of 14 well groups as shown in Fig. 7, this block has rugged and complex terrain. The grey area indicates the obstacles and is unsuitable for installing pipeline and stations. The black dots in the figure indicate the well group locations, and the output of well group is shown in Table 7. The red square indicates the position of FPSO. All produced liquid must be transferred to the FPSO. The platform costs, pipeline data and the pressure increment and dehydrating facilities costs are the same as example 1, shown in Tables 2–4. The property of the produced liquid is shown in Table 5. The results are shown in Fig. 8. The pipeline network after optimization meets all constraints requirements. The pipe length of each pipeline diameter is shown in Table 8. The implementation result shows there is no need for pressure increment and dehydrating facilities. It is analyzed that the pipeline of this block is short and the pressure increment is unnecessary as the
Table 3 Pipeline data.
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Fig. 6. Dot pressure of the network in example 1. Note: Pipe 8-0 denotes the pipe between node 8 and 0 (terminal).
Fig. 4. Optimal result of offshore oilfield gathering system of case one. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Table 6 Pipe length of example 1. Diameter
6 in.
8 in.
10 in.
12 in.
14 in.
Length (km)
12.1
3.0
0
7.8
0
wellhead pressure can satisfy the liquid lift to the terminal FPSO. Meanwhile, there are dehydrating facilities on the terminal FPSO for unified processing thus they are unnecessary to be set on platforms. In the light of the existing topology of the pipeline network, the PIPESIM modelling interface is shown in Fig. 9. The dot pressure is shown in Fig. 10, which indicated the result can satisfy the requirement.
Fig. 7. Oilfield wellhead and FPSO position of example 2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
heuristic algorithm for deep-water gathering system. The problem can be approximately perceived as that to be solved in this paper. Although the heuristic algorithm can quickly solve the model, it isn’t a global search algorithm and thus the optimality of the calculational result still need further discussion. Zhang et al. (2015) adopted an improved genetic algorithm to optimize the topological structure of coal-bed methane gathering pipeline networks. And the algorithm, which is used
4.3. Method comparison According to literatures, there are few researches on optimization of offshore oilfield gathering system. The corresponding modification to other algorithms for gathering pipeline optimization can also solve this kind of problem. For instance, Wang et al. (2012) put forward a
Fig. 5. Modelling interface of PIPESIM in example 1.
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Table 7 Well group output of example 2. No.
Output (m3/d)
No.
Output (m3/d)
1 2 3 4 5 6 7
1520 2480 6110 2800 3110 3680 2340
8 9 10 11 12 13 14
3180 2460 1310 4890 5630 2460 2310
Fig. 10. Dot pressure of the network in example 2.
for solving the connection mode of combination of well tandem and valve, can be modified and applied to optimize the offshore oilfield gathering system. The genetic algorithm is a global search algorithm but it will easily converge to the locally optimal solution if the model has strong nonlinearity. Duan et al. (2016) proposed a two-stages method based on Zhang et al. (2015), considering geographic factors. Firstly, he applied the improved genetic algorithm to solve the twodimensional optimal topology of pipeline networks. And then based on this, he took the three-dimensional terrain into account and used the ant colony algorithm for further resolution. The method can work out the optimization considering complex terrain, but it is still easy to converge to the locally optimal solution. In order to testify the optimization effect of the proposed method, this paper takes methods from Wang et al. (2012), Zhang et al. (2015) and Duan et al. (2016) to carry out the same example. On account of the disadvantage of three methods referred above, there is a penalty function added solving the problem to make the comparison more objectively. The calculation results are shown in Fig. 11. In example one, the proposed method can save 7.1 million dollar, 21.5 million dollar and 12.0 million dollar for investment compared with the others respectively. While in example two, 8.8 million dollar, 15.1 million dollar and 10.0 million dollar can be saved. Since the algorithm is the global optimization, it avoids the poor applicability, the unstable calculation results and the deviation in calculation effects in the previous intelligence algorithm and heuristic algorithm. The algorithm can be easily applied to solving optimization models of offshore oilfield gathering system.
Fig. 8. Optimal result of offshore oilfield gathering system of example 2.
Table 8 Pipeline length of example 2. Diameter
6 in.
8 in.
10 in.
12 in.
14 in.
Length(km)
12.1
15.9
4.8
0
0
Fig. 11. Comparison of three algorithms. Fig. 9. Modelling interface of PIPESIM in example 2.
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