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Tactical planning of offshore petroleum production
European Journal of Operational Research 176 (2007) 550–564 www.elsevier.com/locate/ejor
O.R. Applications
Tactical planning of offshore petroleum production Nina Linn Ulstein a
a,*
, Bjørn Nygreen a, Jan Richard Sagli
b
Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Alfred Getz vei 3, Trondheim N-7491, Norway b Statoil TEK, Process Control, Trondheim N-7005, Norway Received 26 July 2004; accepted 2 June 2005 Available online 6 December 2005
Abstract This paper describes a model for tactical planning of Norwegian petroleum production. The problem involves regulation of production levels from wells, splitting of production flows into oil and gas products, further processing of gas and transportation in a pipeline network. Blending and processing of gas is necessary to satisfy quality requirements in the markets. The problem is formulated with multi-component flows, regulation alternatives in production, non-linear splitting for chemical processing and linear quality constraints on composite products. Production and splitting are modelled with integer requirements. The model is implemented in XpressMP with a Visual Basic supported user interface in Excel. It is constructed in cooperation with the major Norwegian oil company, Statoil and can identify optimal production patterns and assist in planning of possible shut-downs, demonstrate system robustness to customers and aid in contract negotiations. 2005 Elsevier B.V. All rights reserved. Keywords: Decision support systems; Petroleum production; Integer programming
1. Introduction Norway is the worldÕs third largest exporter of crude oil and pipeline gas. Each year, more than 60 billion standard cubic meters of natural gas *
Corresponding author. Tel.: +47 73 59 36 14; fax: +47 73 59 36 03. E-mail addresses: [email protected] (N.L. Ulstein), [email protected] (B. Nygreen), [email protected] (J.R. Sagli).
and 1.2 billion barrels of crude oil are extracted from reservoirs in the continental shelf. In 2003, sales of petroleum products generated an export value of 297 billion NOK (The Ministry of Petroleum and Energy, 2004). The production of natural gas in Norway started in 1977, and a rapid growth has made it one of NorwayÕs main export products. The growth was supported by the building and expansion of a pipeline system for transportation of gas to land-based processing plants and to the European market. The first two
0377-2217/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.06.060
N.L. Ulstein et al. / European Journal of Operational Research 176 (2007) 550–564
pipelines connected the Ekofisk platform to Emden in Germany and the Frigg platform to St. Fergus in Scotland. By 1999, the network included three additional pipelines to Continental Europe and two additional pipelines to Great Britain. Now, fields all along the coast and on-shore
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processing plants in Norway are connected to the network (see Fig. 1, The Ministry of Petroleum and Energy, 2004). Possible developments of natural gas sales involve a 60% increase of the year 2003 level within the next seven years. The main constraints in the gas production network are
Fig. 1. Map of the pipeline network for natural gas transport.
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production capacity, network capacity, processing capacities and market demand. Although there will be expansions in the pipeline network and production capacity, increased delivery plans will reduce free capacity and thereby increase the need for planning and control. This paper describes a model for tactical planning of Norwegian petroleum production. The model was constructed in collaboration with the oil company, Statoil, which owns shares in all petroleum fields in the Norwegian sector. Most fields have several owners. The model maximises the combined profit before tax from all the owners and gives the optimal steady state solution for petroleum production in the Norwegian sector. The model considers regulation of production output from reservoirs, processing of gas in processing plants and routing of gas in the pipeline network. This includes decisions on how much to supply to each spot market while fulfilling long term contract obligations. Due to problem characteristics, the model is implemented as a mixed-integer program. It is constructed to help Statoil optimise production and prepare for major changes and disruptions in the production network and in market demand. In the next section we discuss other contributions that support planning in the oil and gas industry. In Sections 3 and 4 we describe special features of the problem considered and the mathematical model formulation. The user interface and model implementation are described in Section 5. In Section 6 we present and discuss the results in a selection of case studies. Finally, we give some comment on the outcome and on the experiences from the project in Section 7.
2. Literature Reviewing the history of mathematical programming (MP) in the petroleum industry, Bodington and Baker (1990) report on applications for a wide range of planning problems. They also offer interesting insights into how real world problems in the industry motivated early algorithmic developments and improvements in data management and matrix generation routines. Although
using MP in the 1950s and 1960s was cumbersome, most large petroleum companies used it extensively. This is also demonstrated in an early review by Garvin et al. (1957) which describe MP tools for exploration, field development, refining, distribution and marketing. In the Norwegian petroleum industry, early applications include models for reservoir management (Haugland et al., 1988) and for infrastructure planning. Nygreen et al. (1998) describe an infrastructure planning model which had been used by the Norwegian Petroleum Directorate for more than 15 years to plan investments in new fields and pipelines. Jørnsten (1992) and Haugen (1996) applied stochastic programming approaches to the same problem considering uncertainty in respectively demand and field size, while Jonsbra˚ten (1998) introduced stochastic considerations in reservoir development. The long term focus was motivated by the cost structure of offshore petroleum production, which is characterised by high investment costs for construction of pipes and platforms and relatively low variable costs. However, Christiansen and Nygreen (1993) show that there are also great potentials in improved short term planning. Their model controls production from wells in a offshore network of platforms and pipelines. Applications reported in literature often consider planning problems within limited parts of a larger production network. For example; Lee and Aronofsky (1958) report on planning of crude-oil production, Go¨the-Lundgren et al. (2002) describe production scheduling at a refinery and De Wolf and Smeers (2000) describe an application for acquisition and transmission of gas in a pipeline network. However, Bodington and Baker points out that there is a tendency towards integrated planning across multiple units in the network. When Klingman et al. (1987) recount their work in Citgo Petroleum corporation they emphasise how integrated planning across acquisition, refinery and sales operations led to great savings. Often, sub-system optmisation is a result of ownership issues, as few companies have access to information and decision power in all parts of a production network. In our case, Statoil owns shares in large parts of the network, and is con-
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cerned with total network optimisation. To our knowledge, no other applications model the complete production system with multi-component flows, decisions on production from wells, network routing, chemical processing decisions in landbased plants and sales in markets with a number of quality restrictions.
3. Petroleum production The production flow from a well consists mainly of hydrocarbons, water, nitrogen, carbon dioxide and sulphur (see Fig. 2). In general, heavy hydrocarbons contain most energy and are more valuable. They dominate in oil while lighter components form natural gas liquids (NGL) and even more volatile components form natural gas. Natural gas with some content of NGL are called rich gas, while natural gas with little content of NGL are referred to as dry gas. As Fig. 3 illustrates, natural gas is generally transported to shore in pipes, while heavier petroleum products can more easily be transported by ships. Compressors increase the gas pressure to transport gas through the pipelines. The gas itself is used as fuel for the compressors. Norwegian gas originates from a number of sources with substantial variations in quality.
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The quality is determined by the chemical composition. Some quality measures are related to the content of single components while others relate to weighted sums of multiple components. Blending gas from different sources and processing of gas is necessary to satisfy customers quality requirements. Processing of gas is usually achieved through multiple distillation processes where heavier components are separated from lighter components. The model includes offshore processing of the well-flow at platforms and on-shore processing of the rich gas in processing plants. Shutdowns in the network for repair and restoration work and variations in demand due to seasonal changes, increase the need for good planning to sustain a stable quality on the gas deliveries.
4. Modelling Simplicity and flexibility are emphasised in the construction of both the logical model and the user interface. This is done to improve communication with users and to facilitate adjustments of the model to continuous changes in the production network. To enable variable processing of gas into different products and to model quality constraints, flows are modelled as multi-component. Ethane Propane
Methane
iso-Butane Carbon Dioxide n-Butane
Nitrogene Water
iso-Pentane Heptanes_plus
n-Pentane Hexanes
Fig. 2. Example of the chemical composition of a production flow from a well given in mole fractions of each component. The largest fraction is methane which is the dominating component in natural gas.
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Production platform
Processing plant
Oil
Rich gas
NGL products : Ethane Propane Butanes Pentanes Condensate
Gas terminal
Dry gas
Fig. 3. The well flow is separated into rich gas and crude oil at the platform. Rich gas is transported in pipelines while oil is transported by ships. NGL products such as ethane, propane, butanes, pentanes and condensate are separated from the gas at processing plants. The dry gas with about 90% methane is then transported in pipelines to European markets.
4.1. Model structure and notation The model is constructed with a few rigid building blocks. These are combined to express the more complex real world processes in the problem. The rigidity supports a standardised and flexible data input and gives a simple model formulation with few general constraints, rather than many specific constraints. This contrasts the earlier approach by Christiansen and Nygreen (1993). Analysing and breaking up complex real world processes results in four basic processes: production, blending, splitting and sales. The corresponding building blocks are illustrated in Fig. 4. The production network is defined on a directed graph with a set of nodes N and a
A
B
set of arcs A. Each network node i 2 N has an associated property which indicates its function in the network. A restrictive structure limits the number and types of input and output flows of the nodes. The set of production nodes NP N model flows entering the system (Fig. 4A). Production nodes can have any number of inflows, but only one outflow. Only production flows can enter a production node. The set of collection nodes NQ N are nodes for blending flow (Fig. 4B). Collection nodes can have any number of inflows but only one outflow. NR N is the set of nodes for splitting flow (Fig. 4C). To simplify data structure and to give a generic model formulation, all splitting nodes have one inflow and two outflows. Hence, splitting a flow into more than two flows
C
D
Fig. 4. The model and data structure is based on four different types of nodes. Nodetype A, models production, type B models collection, type C models splitting of flow and type D models sales and fuel gas consumption.
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requires a sequence of splitting nodes (see Fig. 12 in Section 7). Finally, NS N is the set of sales nodes (Fig. 4D). Sales nodes have only one inflow and are the only nodes where flows exit the system. For nodes i 2 NP [ NQ with only one successor, this successor is denoted by f(i). Otherwise, the first successor is denoted by f1(i) and the second by f2(i). For nodes i 2 NR [ NS with only one inflow, the predecessor is uniquely defined as f1(i). Let K denote the set of components and k denote a particular component or a collection of similar components. Variables xkij ; ði; jÞ 2 A; k 2 K denote mole flow of component k from node i to j. The following paragraphs describe constraints on network capacity and on each node type. 4.2. Network capacity The maximum mole flow in a pipeline depends on the maximum input pressure and the minimum output pressure for the pipeline. The flow capacities are published in a consistent way by the pipeline operator company Gassco (2004). They may vary due to equipment breakdowns or from changes in the operation of the system. In a given pipeline ði; jÞ 2 A, the sum of component flows cannot exceed the pipeline capacity cij as expressed in (1): X xkij 6 cij 8ði; jÞ 2 A. ð1Þ k2K
4.3. Regulation of production from wells Technical production constraints determine the regulation of production from a source t 2 T, where T is the set of all production sources. A production source can be a well, a group of wells, a field or exogenously given. Grouping production flows from wells is possible when flows have equal chemical properties and wells are subject to the same regulation restrictions. Grouping can also be a result of limited detail in available information. This can be the case when another company than Statoil is the operator of a platform. Reservoir simulation and optimisation models determine a set of rules for regulating production
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from a source. They aim to maximise the output of oil and gas during the lifetime of the reservoir by using an optimal operating pressure (see Haugland et al., 1988). Regulation restrictions vary among sources. The alternative regulation methods for production output from a source are: • • • •
Fixed to a specific level: fixed. Between bounds: continuous. Zero or at a fixed level: binary. Zero or between bounds: semi continuous.
These regulation regimes are formulated as bounds on the production variables yt, t 2 T. For easier interpretation of results, the production variables denote the production output as fraction of total production capacity bt. Hence, yt is in the interval zero to one. The subset Ti T is the set of all sources t connected to production node i 2 NP . Eq. (2) states that the component flows xkij from node i equal the sum of production from all sources connected to production node i 2 NP . Here, rkt expresses the mole fraction of component k 2 K in production source t 2 T. Within the production bounds specified, the composition from each source is assumed constant: X xkij bt rkt y t ¼ 0 8i 2 NP ; j ¼ f ðiÞ; k 2 K. t2Ti
ð2Þ Splitting of flow from a well into oil and natural gas is fixed at most platforms due to characteristics of the production equipment. When the splitting is fixed and no binding constraints apply to oil output alone, the value of associated oil is calculated as part of the pre-processing of data, and included in the objective function. Then, rkt gives the mole fractions of only gas from the source. When there are alternative ways to split oil and gas, or constraints on oil output alone, rkt gives the mole fractions of both oil and gas. Then the mixed flow is processed at splitting nodes. For variable splitting, the optimisation selects optimal splitting into oil and gas. The separated oil is sent directly to market nodes and priced according to the chemical composition and transport costs from the production platform. Restrictions on oil output result mainly from limited capacity for separating water,
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or limited transport capacity for oil. The model assumes infinite demand for crude oil. This is possible as the spot-market for crude oil is wellfunctioning. 4.4. Mass conservation at blending nodes Mass conservation at blending nodes is expressed in Eq. (3). Since, there is only one successor node j = f(i), to a blending node i, the flow of component k from node i is equal to the sum of inflows of that component to node i: X xkij xkhi ¼ 0 8i 2 NQ ; j ¼ f ðiÞ; k 2 K.
the inflow node i. Binary variables kmi force all but one set of jKj dummy flow variables wkm hi to zero. This way, exactly one set m of split-fractions will be used. For a given splitting node i 2 NR , the optimisation selects the split-fractions akm of the i inflow xkhi to send into the first pipe xkij in Eq. (6). The flow in the second pipe xkig is determined by the mass balance in Eq. (4): xkhi ¼ xkij þ xkig
8i 2 NR ; h ¼ f 1 ðiÞ;
j ¼ f1 ðiÞ; g ¼ f2 ðiÞ; k 2 K; xkhi
X
wkm hi ¼ 0
ð4Þ
8i 2 NR ; h ¼ f 1 ðiÞ; k 2 K;
m2M
hjðh;iÞ2A
ð5Þ
ð3Þ 4.5. Splitting of flow The splitting of a flow is either homogenous or heterogenous. In homogenous splitting, the same split-fraction applies to all components. Then the quality of the two resulting flows is equal to that of the original flow. This is the case in sub-sea splitting, where valves control how much goes in either direction. In heterogenous splitting, different split-fractions apply to each component. Lighter components can be separated from heavier components in separators where the fractions removed depend on the temperature and pressure applied. Heterogenous splitting requires one or more separation processes. Regulation of one process influences the outcome of the next, creating a system of non-linear relationships. Due to equipment characteristics such as high and low bounds on operating temperature for each separator, these functions are not continuous. In the model, heterogenous splitting is formulated as discrete choices between feasible split-fractions. Each set m 2 M R includes split-fractions akm i ; i 2 N for all components k 2 K, which express the ratio of each component to separate at the split node. Thus, for heterogenous splitting one need to select among jMj sets of split-fractions on all components. Eqs. (4)–(9) describe heterogenous splitting at a node i 2 NR where the first outflow goes to node j, and the second goes to node g. For each possible splitting m we define dummy variables wkm hi for
xkij
X
km akm i whi ¼ 0
8i 2 NR ; h ¼ f 1 ðiÞ;
m2M
j ¼ f1 ðiÞ; k 2 K; X
ð6Þ
m wkm 8i 2 NR ; hi chi ki 6 0
k2K
h ¼ f 1 ðiÞ; m 2 M; X
kmi ¼ 1
8i 2 NR ;
ð7Þ ð8Þ
m2M
kmi 2 f0; 1g 8i 2 NR ; m 2 M.
ð9Þ
Restriction (7) could have been formulated with upper capacity bounds on each component, but with varying flow composition it is difficult to get good bounds. Therefore, total flow capacity is used. Similar expressions as described above apply to homogenous splitting, but then the split-fraction is independent of component since the same fraction applies to all components. This could have been implemented by non-linear constraints, but to support the simple implementation with a few general building blocks and constraints, homogenous splitting was also formulated as a choice between sets of candidate split-fractions. 4.6. Market requirements The total flow to a sales node j 2 NS is limited by upper and lower bounds on demand, denoted by lj and uj respectively (10):
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lj 6
X
xkij 6 uj
8j 2 NS ; i ¼ f 1 ðjÞ.
ð10Þ
k2K
In addition, the quality of the flow must respect all quality requirements. Some quality requirements apply to groups of components, while others apply to single components. General quality restrictions for sales nodes are expressed by Eqs. (11) and (12). Here dkq is the weight for component k in quality measure q 2 Q, where Q is the set of all quality restrictions. The quality is restricted by a lower bound lijq and/or an upper bound uijq. Most quality restrictions apply to sales nodes, but similar restrictions can be specified for any network flow: X k X dq xkij lijq xkij P 0 8j 2 NS ; k2K
k2K
i¼f X k2K
1
ðjÞ; q 2 Q;
dkq xkij uijq
X
xkij 6 0
ð11Þ 8j 2 NS ;
k2K
i ¼ f 1 ðjÞ; q 2 Q.
products (13). To treat all products in all markets in a similar way, prices are expressed as unit prices, pkj , that may vary both with component k 2 K and market j 2 NS . Crude oil and NGL customers pay a weighted price dependent on the chemical composition of the product. This is modelled by letting the price pkj vary with k. Natural gas customers have such strict quality requirements that they pay per standard flow units delivered. Thus, pkj is independent of k in natural gas markets. For fixed splitting of oil and gas at platforms, the value of associated oil can be calculated as part of the pre-processing of data. This value depends on the oilÕs chemical composition and on the transport costs from the platform. The cost of producing from source t 2 T, adjusted for the value of oil, is denoted by xt. Production costs from different sources vary due to economies of scale and differences in production equipment: X X X X max z ¼ pkj xkij xt bt y t . ð13Þ i2N j2NS k2K
ð12Þ
Customers limit the energy content of the gas to ensure stable operating conditions in their processing plants and equipments. The energy content or gross calorific value (GCV) is equal to the weighted average of the potential energy of all components k 2 K. For this quality restriction q 2 Q, the dkq parameters in Eqs. (11) and (12) are equal to the potential chemical energy for each component k. The lower bound lijq and upper bound uijq, restrict minimum and maximum energy content. Customers also limit the relative content of single components such as carbon dioxide in the gas. High levels of carbon dioxide may cause erosion problems and some countries impose environmental taxes on emissions of the gas. In Eq. (12) this quality restriction q 2 Q has dkq ¼ 1 for k = carbon dioxide and dkq ¼ 0 for all other components. The maximum relative carbon dioxide content in the flow is limited by the upper bound uijq. There is no lower bound. 4.7. Objective function The model maximises the net income before taxes from the production and sale of petroleum
557
t2T
Fuel gas is consumed to transport gas to markets. As production of oil and NGL are limited by the demand for associated gas, Statoil could choose to maximise fuel gas consumption and thereby produce more oil and NGL. However, the government has regulated this condition by imposing a tax for fuel gas consumption. Fuel gas is sent to market nodes with negative prices equal to the taxes for fuel gas emissions. The compression work required to transport gas through a pipeline is a non-linear function of the gas flow. Consumption of fuel gas can be linearised within the range of permitted gas flow levels which is bounded by maximum gas flow capacity cij. As Fig. 5 shows, linearisation of the fuel gas consumption introduces errors, but this is considered acceptable as fuel gas consumption is less than 2% of the total gas production.
5. Implementation Database and reporting of results are implemented in a Visual Basic supported user interface in Excel. The software choice is based on plannerÕs preferences. The planner presses a macro-button in
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Fuel gas consumption
real model
Total flow Fig. 5. Real and approximated (model) fuel gas consumption in a compressor as a function of the gas flow.
the workbook to start XpressMP (Dash Associates, 2002) which reads input data, generates the matrix, optimises the problem and writes results back into the spreadsheet (see Fig. 6). Data are grouped in modules in the Excel workbook. The main module contains the most critical information and has links to all other modules. There are macro-buttons for navigating in the
database and for various data processing. All data processing operations are done in the spreadsheets. The model is formulated in the algebraic modelling language in XpressMP. The model can read data either directly from the spreadsheets or from .dat files automatically generated from the workbook. The latter alternative proved faster. Pre-processing of data supports a simple and generic model formulation and reduces the size of the matrix. For example, the number of variables is reduced by calculating the value of associated oil and NGL at platforms with fixed split and subtracting this value from the variable production costs, rather than modelling this as a fixed splitting node. Choices between discrete split-fractions are formulated by binary variables kmj and kkm j (see Section 4.5). The split-fractions can be sorted in a logic order for all splitting nodes. For homogenous splitting, they are simply sorted according to increasing fraction sent to the first successor node. For heterogenous splitting, it is a bit more complex. Here the order depends on both the fraction sent to the first successor node and on the rel-
1 Run optimisation
5 Write and present results in workbook
Excel workbook
Results files
4 Optimise and output solution
2 Write data to files
Model file
Matrix
3 Generate matrix
Fig. 6. Schematic representation of the optimisation process and the data handling involved.
N.L. Ulstein et al. / European Journal of Operational Research 176 (2007) 550–564
559
Troll
Åsgard A4 C B
39 49
29
Åsgard Transport
Statfjord Gullfaks
Kollsnes
48.1
Zeepipe IIA Heimdal
Statpipe
Condensate products
28.4
60
G TSSleipnerAH
Zeepipe IIB 31.6
11
R
9.7
Kårstø Statpipe E S Draupner Draupner Ekofisk
Europipe II 56.7
Dunkerque
Norpipe
Norfra
Zeepipe I Zeebrugge
18 Europipe I 23.8
Norsea
Netra
EMS
Optimal solution
39.5
22.3
21.7
42.4
47.1
Market demand
39.5
23.8
21.7
42.4
47.1
Fig. 7. Process flow sheet with results for the standard scenario. The oval nodes are platforms which collect flow from a number of connected wells. The lines are pipelines for transport to processing plants and to markets. The rectangles represent processing plants. The blank nodes are market nodes. Production figures are stated in million standard cubic metres per day [MSm3/d]. Figures in gray boxes report daily production of natural gas, while figures next to main pipelines report daily gas transport. The two bottom lines compare the gas sales to the market capacity in the five natural gas markets.
ative content of light components. As such ordering is possible, the binary splitting variables are coded as SOS1 sets (Beale and Tomlin, 1970). Thus, the optimisation process branches on splitting patterns as SOS1 sets. Post-processing data include visual presentation of main results in graphs and in a process flow sheet. Reading results into the results worksheets can be initiated automatically or manually by pressing a macro-button. Detailed results are presented in tables and aggregated results are shown in process flow diagrams as illustrated in Fig. 7.
production patterns are compared to a base case scenario. The base case represents the present network configuration and uses average daily demand data. The base case scenario has 756 continuous variables, 1197 columns, five binary variables, 10 semi-continuous variables, six SOS1 sets and 60 set members. The solution time on an Intel 4-M 1.7 GHz running WindowsXP was 4 minutes. Solution time is comparable for all scenarios. Solutions are presented in tables and process flow sheets. Fig. 7 shows an aggregate flow sheet with the solution for the standard scenario. We see that the model attempts to fulfil all demand for natural gas.
6. Results
6.1. Case 1: Fixed network configuration with demand variations
The model is solved for a number of different scenarios. The scenarios reflect changes in the network and in the demand situation. The suggested
Demand for natural gas varies during the year as consumersÕ need for heating or cooling changes.
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Natural gas production [MSm3/day]
Many consumers use gas directly for heating. For cooling, the gas is first transformed to electricity at gas power plants. To identify optimal production patterns for different demand levels, the model is solved for normal, high and low demand scenarios. Normal demand is equal to average yearly demand. High and low demand equals respectively 110% and 60% of average demand. Fig. 8 shows how natural gas production from fields vary for the three scenarios. The left graph shows total production output and the right graph shows output in percent of total capacity. The production output from an oil field equals the sum of production from wells connected to that field. The capacity of a field is limited by the production capacity from wells, processing capacities at the platform, and the gas pipeline capacity from the platform. In the high demand scenario, all fields except for the Troll and Ekofisk fields, produce at full capacity. When demand decreases, production is first reduced at these same platforms and in addition ˚ sgard. In the low demand scenario, producat A tion is also decreased at Heimdal and Sleipner. Limited demand for natural gas constrains production of associated oil and NGL. Therefore the model maximises production from fields with high rates of associated products. The StatGull field has the highest oil fractions and is therefore selected to produce at full capacity in all scenarios. Troll has low rates of associated oil and is used as a ‘‘swing’’-producer to handle most of the demand variations. Consequently, it has no production at low demand, but supplies 24% of total demand 70 60 50 40 30 20 10 0 Åsgard 60% demand
Troll
StatGull
Heimdal
100% demand
Sleipner
Ekofisk
in the high demand scenario. This general result corresponds to present operational policies for the Norwegian sector. 6.2. Case 2: Fixed demand and varying quality constraints For contract negotiations, it is necessary to know how the customerÕs quality requirements influence profit. To understand the effects of quality restrictions, the model was solved for a number of instances with different quality bounds. Results from changing bounds on the energy content (GCV) of sales gas are presented in Figs. 9 and 10. Here, the GCV bounds were simultaneously changed in the five natural gas market nodes. In each instance, the bounds were tightened or relaxed by a given percentage, relative to present quality restrictions. We assume that the price for natural gas is the same in each instance. The results in Fig. 9 show how total profit decreases with tighter quality requirements. Letters A, B, C and D in the figure refer to instances commented on in the following text. Fig. 9A shows the profit with present quality restrictions. When quality requirements are tightened by 1% (Fig. 9B), profit decreases, but this is not due to lower deliveries of gas. The system still fulfils nearly all natural gas demand (3.4% less in one market). The drop in profit is mostly due to lower output of oil and NGL products. This is because more of the energy-rich components are channelled into the natural gas to fulfil the Production in percent of total capacity
560
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Åsgard
Troll
StatGull
Heimdal
Sleipner
Ekofisk
110% demand
Fig. 8. These graphs show variations in production output from main production platforms for different demand scenarios. The left graph displays total production output while the right graph displays production output in percent of total capacity.
N.L. Ulstein et al. / European Journal of Operational Research 176 (2007) 550–564
561
655 D Objective function value [MNOK/d]
650
A
645
B
640 635
C
630 625 620 615
-2.0%
-1.5 %
-1.0 %
-0.5 %
610 0.0 %
0.5 %
1.0 %
1.5 %
Tightening or relaxation of GCV value requirements in percent
44
44
43
43
42
42
41
41 Kj/Sm3
Kj/Sm3
Fig. 9. Changes in the objective value as a function of the GCV quality requirements.
40
Optimial value Lower bound
40
Upper bound
39
39
38
38
37
37 36
36
Norsea
EMS
Netra
Dunkerque Zeebrugge
Scenario A, present GCV requirements
Norsea
EMS
Netra
Dunkerque Zeebrugge
Scenario C, 1.5% tighter GCV requirements
Fig. 10. Optimal GCV values for gas delivered in markets with different quality bounds in scenarios A and C.
GCV requirement. Further tightening of quality requirements, makes it infeasible to deliver natural gas in some markets. Then incomes from sales of both natural gas and associated oil and NGL decrease (Fig. 9C). Fig. 10 shows the GCV value of product delivered in five market nodes, for instances A and C from Fig. 9. In most cases, the optimal GCV value
for natural gas in the markets is close to the lower bound, as high energy components are more valuable if they are channelled into other products. The upper bound is only constraining if processing equipment cannot separate these components (Fig. 10C, Zeebrugge). This indicates possibilities to increase profit by installing better processing equipment.
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Also note that wider GCV bounds only give a slight improvement in profit (see Fig. 9D). This is because not much more of the energy-rich components can be extracted from the gas, with the existing processing equipment. Therefore the company should not pay for looser quality constraints. Also, customers should pay substantially more for higher quality gas. 6.3. Case 3: Contingency plans for system breakdown There are system breakdowns every year. The model can find new feasible and optimal production patterns to prepare for such breakdowns. At one point during the testing phase of the model, the workersÕ union threatened to go on strike and to close down the main gas production field, Troll, until their salaries were raised. This scenario was tested to see if new feasible solutions could be achieved. Unfortunately, Troll proved to be such an important gas producer, that some of the gas contracts could not be serviced. However, by using wells with low content of other petroleum products and more natural gas content, the remainder of the system was able to supply 96% of the demand. Fig. 11 shows how the production levels from wells change if Troll is closed.
7. Discussion and conclusion Simple building blocks with restrictive structures enable a generic and simple model formula-
tion. At the same time, the rigid structure increases the total number of nodes and flow variables. Fig. 12 illustrates how a direct formulation in (a), can be replaced by three standard blocks in (b), one collection block B, and two splitting blocks C. This increases the number of flow variables or arcs, but does not increase the number of split fractions, a1 and a2 versus b1 and b2. In the generic approach, there is one constraint for each building block type and combinations of these model the various real world processes. This greatly reduces the size of the model formulation compared to a more specific model. In a large and complex production system, this approach reduces the risk of errors in the formulation, and improves the ability to change the network by removing or adding pipes, nodes, sources or processing equipment. This functionality is an advantage in evaluating system breakdowns and possible system extensions. Planning tools for petroleum production can be divided into strategic, tactical and operational tools, according to their timeframe. Based on how they function, they can be further divided into optimisation and simulation based tools. Statoil uses an optimisation tool to support long term planning, similar to the one described by Nygreen et al. (1998), and are currently implementing an optimisation tool for detailed day-to-day planning. The model described here considers tactical planning and disruptions planning and is constructed to replace simulation based tools. Tactical planning consists of choosing a relatively stable production pattern to be maintained for some
Fig. 11. Production from 26 wells in one scenario with Troll producing at normal capacity (base case) and in the scenario with Troll closed due to a strike.
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(b)
(a)
B
C
α1
α2
1-α 1 - α 2
β1
1-β 1 C
β2
1-β 2
Fig. 12. Comparison between a specific modelling approach illustrated in (a) and a generic modelling approach illustrated in (b).
period of time, and disruption planning consist of identifying alternative ways to satisfy customers demand for shut-downs in parts of the system. In both cases, operators can limit the difference between the original and the new solution for production and splitting variables or add penalties on reduced sales. Still, the transition effort is often negligible in comparison to the benefit of using the optimal production pattern. Long term planning determines production regulation bounds that ensure long term optimality. Within these bounds, the tactical planning model will produce the most valuable petroleum first, and distribute petroleum components on products to maximise production of most valuable products. Assuming that all available petroleum resources will be exploited, less valuable petroleum will be used later. Thus, producing from sources with the most valuable petroleum first, only contributes to the long term profit by the depreciation of the higher value from these sources. The real value contribu-
tion from tactical planning comes from improving the way flow from the wells is processed and distributed on different products and markets. This requires careful planning of the processing and the regulation of production from sources to get the right quality. Tests showed that the total profit was strongly influenced by only small changes in quality requirements. This information is useful in contract negotiations to determine right prices for gas of different quality. Statoil suggested that the model could also be used to demonstrate the safety of stable deliveries to customers. If Statoil can demonstrate alternative ways to secure supply in case of a breakdown, this may increase customersÕ willingness to buy Norwegian gas. When the oil-workersÕ union threatened to close down production at the main gas production field, the model showed that by changing the production pattern, most demand could still be satisfied. This result demonstrates system robustness to customers.
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The main benefit of the model tool discussed here is the possibility to identify radically new ways to satisfy demand for varying network configurations. Alternatively this analysis is done by experts with profound knowledge of the network, checking the feasibility of new production patterns by combining results from several local simulation models. This is a cumbersome process which does not easily produce non-intuitive solutions. It is also hard to even identify feasible solutions without using optimisation, since most changes require very detailed adjustments across the system. The user interface improved communication with users both during the modelling process and after. Their possibility to access, understand and alter datainput supported the credibility of the model. Graphical presentation of results was in particular effective for communication with users that were not directly involved in the modelling process. References Beale, E.M.L., Tomlin, J.A., 1970. Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. In: Lawrence, J. (Ed.), Proceedings of the Fifth International Conference on Operational Research. Tavistock Publications, London, pp. 447–454. Bodington, C.E., Baker, T.E., 1990. A history of mathematical programming in the petroleum industry. Interfaces 20 (4), 117–127. Christiansen, M., Nygreen, B., 1993. Well management in the North Sea. Annals of Operations Research 43, 427– 441.
Dash Associates, 2002. XpressMP Essentials—An Introduction to Modeling and Optimization. Northants, UK. De Wolf, D., Smeers, Y., 2000. The gas transmission problem solved by an extension of the simplex algorithm. Management Science 46 (11), 1454–1465. Garvin, W.W., Crandall, H.W., John, J.B., Spellmann, R.A., 1957. Applications of linear programming in the oil industry. Management Science 3 (4), 407–430. Gassco, A.S., 2004. Haugesund, Norway. URL: http://www. gassco.no, last date accessed: 27 April.. Go¨the-Lundgren, M., Lundgren, J.T., Persson, J.A., 2002. An optimization model for refinery production scheduling. International Journal of Production Economics 78, 255– 270. Haugen, K., 1996. A Stochastic dynamic programming model for scheduling of offshore petroleum fields with resource uncertainty. European Journal of Operational Research 88 (1), 88–100. ˚ ., Asheim, H., 1988. Models for Haugland, D., Hallefjord, A petroleum field exploitation. European Journal of Operational Research 37 (1), 58–72. Jonsbra˚ten, T.W., 1998. Oil field optimization under price uncertainty. Journal of the Operational Research Society 49, 811–818. Jørnsten, K.O., 1992. Sequencing offshore oil and gas fields under uncertainty. European Journal of Operational Research 58 (2), 191–201. Klingman, D., Phillips, N., Steiger, D., Young, W., 1987. The successful deployment of management science throughout Citgo Petroleum Corporation. Interfaces 17 (1), 4–25. Lee, A.S., Aronofsky, J.S., 1958. A linear programming model for scheduling crude oil production. Journal of Petroleum Technology (July), 51–54. Nygreen, B., Christiansen, M., Haugen, K., Bjørkvoll, T., Kristiansen, Ø., 1998. Modeling Norwegian petroleum production and transportation. Annals of Operations Research 82, 251–267. The Ministry of Petroleum and Energy, 2004. Facts 2004 Norwegian Petroleum Activity, Oslo, Norway.
O.R. Applications
Tactical planning of offshore petroleum production Nina Linn Ulstein a
a,*
, Bjørn Nygreen a, Jan Richard Sagli
b
Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Alfred Getz vei 3, Trondheim N-7491, Norway b Statoil TEK, Process Control, Trondheim N-7005, Norway Received 26 July 2004; accepted 2 June 2005 Available online 6 December 2005
Abstract This paper describes a model for tactical planning of Norwegian petroleum production. The problem involves regulation of production levels from wells, splitting of production flows into oil and gas products, further processing of gas and transportation in a pipeline network. Blending and processing of gas is necessary to satisfy quality requirements in the markets. The problem is formulated with multi-component flows, regulation alternatives in production, non-linear splitting for chemical processing and linear quality constraints on composite products. Production and splitting are modelled with integer requirements. The model is implemented in XpressMP with a Visual Basic supported user interface in Excel. It is constructed in cooperation with the major Norwegian oil company, Statoil and can identify optimal production patterns and assist in planning of possible shut-downs, demonstrate system robustness to customers and aid in contract negotiations. 2005 Elsevier B.V. All rights reserved. Keywords: Decision support systems; Petroleum production; Integer programming
1. Introduction Norway is the worldÕs third largest exporter of crude oil and pipeline gas. Each year, more than 60 billion standard cubic meters of natural gas *
Corresponding author. Tel.: +47 73 59 36 14; fax: +47 73 59 36 03. E-mail addresses: [email protected] (N.L. Ulstein), [email protected] (B. Nygreen), [email protected] (J.R. Sagli).
and 1.2 billion barrels of crude oil are extracted from reservoirs in the continental shelf. In 2003, sales of petroleum products generated an export value of 297 billion NOK (The Ministry of Petroleum and Energy, 2004). The production of natural gas in Norway started in 1977, and a rapid growth has made it one of NorwayÕs main export products. The growth was supported by the building and expansion of a pipeline system for transportation of gas to land-based processing plants and to the European market. The first two
0377-2217/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.06.060
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pipelines connected the Ekofisk platform to Emden in Germany and the Frigg platform to St. Fergus in Scotland. By 1999, the network included three additional pipelines to Continental Europe and two additional pipelines to Great Britain. Now, fields all along the coast and on-shore
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processing plants in Norway are connected to the network (see Fig. 1, The Ministry of Petroleum and Energy, 2004). Possible developments of natural gas sales involve a 60% increase of the year 2003 level within the next seven years. The main constraints in the gas production network are
Fig. 1. Map of the pipeline network for natural gas transport.
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production capacity, network capacity, processing capacities and market demand. Although there will be expansions in the pipeline network and production capacity, increased delivery plans will reduce free capacity and thereby increase the need for planning and control. This paper describes a model for tactical planning of Norwegian petroleum production. The model was constructed in collaboration with the oil company, Statoil, which owns shares in all petroleum fields in the Norwegian sector. Most fields have several owners. The model maximises the combined profit before tax from all the owners and gives the optimal steady state solution for petroleum production in the Norwegian sector. The model considers regulation of production output from reservoirs, processing of gas in processing plants and routing of gas in the pipeline network. This includes decisions on how much to supply to each spot market while fulfilling long term contract obligations. Due to problem characteristics, the model is implemented as a mixed-integer program. It is constructed to help Statoil optimise production and prepare for major changes and disruptions in the production network and in market demand. In the next section we discuss other contributions that support planning in the oil and gas industry. In Sections 3 and 4 we describe special features of the problem considered and the mathematical model formulation. The user interface and model implementation are described in Section 5. In Section 6 we present and discuss the results in a selection of case studies. Finally, we give some comment on the outcome and on the experiences from the project in Section 7.
2. Literature Reviewing the history of mathematical programming (MP) in the petroleum industry, Bodington and Baker (1990) report on applications for a wide range of planning problems. They also offer interesting insights into how real world problems in the industry motivated early algorithmic developments and improvements in data management and matrix generation routines. Although
using MP in the 1950s and 1960s was cumbersome, most large petroleum companies used it extensively. This is also demonstrated in an early review by Garvin et al. (1957) which describe MP tools for exploration, field development, refining, distribution and marketing. In the Norwegian petroleum industry, early applications include models for reservoir management (Haugland et al., 1988) and for infrastructure planning. Nygreen et al. (1998) describe an infrastructure planning model which had been used by the Norwegian Petroleum Directorate for more than 15 years to plan investments in new fields and pipelines. Jørnsten (1992) and Haugen (1996) applied stochastic programming approaches to the same problem considering uncertainty in respectively demand and field size, while Jonsbra˚ten (1998) introduced stochastic considerations in reservoir development. The long term focus was motivated by the cost structure of offshore petroleum production, which is characterised by high investment costs for construction of pipes and platforms and relatively low variable costs. However, Christiansen and Nygreen (1993) show that there are also great potentials in improved short term planning. Their model controls production from wells in a offshore network of platforms and pipelines. Applications reported in literature often consider planning problems within limited parts of a larger production network. For example; Lee and Aronofsky (1958) report on planning of crude-oil production, Go¨the-Lundgren et al. (2002) describe production scheduling at a refinery and De Wolf and Smeers (2000) describe an application for acquisition and transmission of gas in a pipeline network. However, Bodington and Baker points out that there is a tendency towards integrated planning across multiple units in the network. When Klingman et al. (1987) recount their work in Citgo Petroleum corporation they emphasise how integrated planning across acquisition, refinery and sales operations led to great savings. Often, sub-system optmisation is a result of ownership issues, as few companies have access to information and decision power in all parts of a production network. In our case, Statoil owns shares in large parts of the network, and is con-
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cerned with total network optimisation. To our knowledge, no other applications model the complete production system with multi-component flows, decisions on production from wells, network routing, chemical processing decisions in landbased plants and sales in markets with a number of quality restrictions.
3. Petroleum production The production flow from a well consists mainly of hydrocarbons, water, nitrogen, carbon dioxide and sulphur (see Fig. 2). In general, heavy hydrocarbons contain most energy and are more valuable. They dominate in oil while lighter components form natural gas liquids (NGL) and even more volatile components form natural gas. Natural gas with some content of NGL are called rich gas, while natural gas with little content of NGL are referred to as dry gas. As Fig. 3 illustrates, natural gas is generally transported to shore in pipes, while heavier petroleum products can more easily be transported by ships. Compressors increase the gas pressure to transport gas through the pipelines. The gas itself is used as fuel for the compressors. Norwegian gas originates from a number of sources with substantial variations in quality.
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The quality is determined by the chemical composition. Some quality measures are related to the content of single components while others relate to weighted sums of multiple components. Blending gas from different sources and processing of gas is necessary to satisfy customers quality requirements. Processing of gas is usually achieved through multiple distillation processes where heavier components are separated from lighter components. The model includes offshore processing of the well-flow at platforms and on-shore processing of the rich gas in processing plants. Shutdowns in the network for repair and restoration work and variations in demand due to seasonal changes, increase the need for good planning to sustain a stable quality on the gas deliveries.
4. Modelling Simplicity and flexibility are emphasised in the construction of both the logical model and the user interface. This is done to improve communication with users and to facilitate adjustments of the model to continuous changes in the production network. To enable variable processing of gas into different products and to model quality constraints, flows are modelled as multi-component. Ethane Propane
Methane
iso-Butane Carbon Dioxide n-Butane
Nitrogene Water
iso-Pentane Heptanes_plus
n-Pentane Hexanes
Fig. 2. Example of the chemical composition of a production flow from a well given in mole fractions of each component. The largest fraction is methane which is the dominating component in natural gas.
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Production platform
Processing plant
Oil
Rich gas
NGL products : Ethane Propane Butanes Pentanes Condensate
Gas terminal
Dry gas
Fig. 3. The well flow is separated into rich gas and crude oil at the platform. Rich gas is transported in pipelines while oil is transported by ships. NGL products such as ethane, propane, butanes, pentanes and condensate are separated from the gas at processing plants. The dry gas with about 90% methane is then transported in pipelines to European markets.
4.1. Model structure and notation The model is constructed with a few rigid building blocks. These are combined to express the more complex real world processes in the problem. The rigidity supports a standardised and flexible data input and gives a simple model formulation with few general constraints, rather than many specific constraints. This contrasts the earlier approach by Christiansen and Nygreen (1993). Analysing and breaking up complex real world processes results in four basic processes: production, blending, splitting and sales. The corresponding building blocks are illustrated in Fig. 4. The production network is defined on a directed graph with a set of nodes N and a
A
B
set of arcs A. Each network node i 2 N has an associated property which indicates its function in the network. A restrictive structure limits the number and types of input and output flows of the nodes. The set of production nodes NP N model flows entering the system (Fig. 4A). Production nodes can have any number of inflows, but only one outflow. Only production flows can enter a production node. The set of collection nodes NQ N are nodes for blending flow (Fig. 4B). Collection nodes can have any number of inflows but only one outflow. NR N is the set of nodes for splitting flow (Fig. 4C). To simplify data structure and to give a generic model formulation, all splitting nodes have one inflow and two outflows. Hence, splitting a flow into more than two flows
C
D
Fig. 4. The model and data structure is based on four different types of nodes. Nodetype A, models production, type B models collection, type C models splitting of flow and type D models sales and fuel gas consumption.
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requires a sequence of splitting nodes (see Fig. 12 in Section 7). Finally, NS N is the set of sales nodes (Fig. 4D). Sales nodes have only one inflow and are the only nodes where flows exit the system. For nodes i 2 NP [ NQ with only one successor, this successor is denoted by f(i). Otherwise, the first successor is denoted by f1(i) and the second by f2(i). For nodes i 2 NR [ NS with only one inflow, the predecessor is uniquely defined as f1(i). Let K denote the set of components and k denote a particular component or a collection of similar components. Variables xkij ; ði; jÞ 2 A; k 2 K denote mole flow of component k from node i to j. The following paragraphs describe constraints on network capacity and on each node type. 4.2. Network capacity The maximum mole flow in a pipeline depends on the maximum input pressure and the minimum output pressure for the pipeline. The flow capacities are published in a consistent way by the pipeline operator company Gassco (2004). They may vary due to equipment breakdowns or from changes in the operation of the system. In a given pipeline ði; jÞ 2 A, the sum of component flows cannot exceed the pipeline capacity cij as expressed in (1): X xkij 6 cij 8ði; jÞ 2 A. ð1Þ k2K
4.3. Regulation of production from wells Technical production constraints determine the regulation of production from a source t 2 T, where T is the set of all production sources. A production source can be a well, a group of wells, a field or exogenously given. Grouping production flows from wells is possible when flows have equal chemical properties and wells are subject to the same regulation restrictions. Grouping can also be a result of limited detail in available information. This can be the case when another company than Statoil is the operator of a platform. Reservoir simulation and optimisation models determine a set of rules for regulating production
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from a source. They aim to maximise the output of oil and gas during the lifetime of the reservoir by using an optimal operating pressure (see Haugland et al., 1988). Regulation restrictions vary among sources. The alternative regulation methods for production output from a source are: • • • •
Fixed to a specific level: fixed. Between bounds: continuous. Zero or at a fixed level: binary. Zero or between bounds: semi continuous.
These regulation regimes are formulated as bounds on the production variables yt, t 2 T. For easier interpretation of results, the production variables denote the production output as fraction of total production capacity bt. Hence, yt is in the interval zero to one. The subset Ti T is the set of all sources t connected to production node i 2 NP . Eq. (2) states that the component flows xkij from node i equal the sum of production from all sources connected to production node i 2 NP . Here, rkt expresses the mole fraction of component k 2 K in production source t 2 T. Within the production bounds specified, the composition from each source is assumed constant: X xkij bt rkt y t ¼ 0 8i 2 NP ; j ¼ f ðiÞ; k 2 K. t2Ti
ð2Þ Splitting of flow from a well into oil and natural gas is fixed at most platforms due to characteristics of the production equipment. When the splitting is fixed and no binding constraints apply to oil output alone, the value of associated oil is calculated as part of the pre-processing of data, and included in the objective function. Then, rkt gives the mole fractions of only gas from the source. When there are alternative ways to split oil and gas, or constraints on oil output alone, rkt gives the mole fractions of both oil and gas. Then the mixed flow is processed at splitting nodes. For variable splitting, the optimisation selects optimal splitting into oil and gas. The separated oil is sent directly to market nodes and priced according to the chemical composition and transport costs from the production platform. Restrictions on oil output result mainly from limited capacity for separating water,
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or limited transport capacity for oil. The model assumes infinite demand for crude oil. This is possible as the spot-market for crude oil is wellfunctioning. 4.4. Mass conservation at blending nodes Mass conservation at blending nodes is expressed in Eq. (3). Since, there is only one successor node j = f(i), to a blending node i, the flow of component k from node i is equal to the sum of inflows of that component to node i: X xkij xkhi ¼ 0 8i 2 NQ ; j ¼ f ðiÞ; k 2 K.
the inflow node i. Binary variables kmi force all but one set of jKj dummy flow variables wkm hi to zero. This way, exactly one set m of split-fractions will be used. For a given splitting node i 2 NR , the optimisation selects the split-fractions akm of the i inflow xkhi to send into the first pipe xkij in Eq. (6). The flow in the second pipe xkig is determined by the mass balance in Eq. (4): xkhi ¼ xkij þ xkig
8i 2 NR ; h ¼ f 1 ðiÞ;
j ¼ f1 ðiÞ; g ¼ f2 ðiÞ; k 2 K; xkhi
X
wkm hi ¼ 0
ð4Þ
8i 2 NR ; h ¼ f 1 ðiÞ; k 2 K;
m2M
hjðh;iÞ2A
ð5Þ
ð3Þ 4.5. Splitting of flow The splitting of a flow is either homogenous or heterogenous. In homogenous splitting, the same split-fraction applies to all components. Then the quality of the two resulting flows is equal to that of the original flow. This is the case in sub-sea splitting, where valves control how much goes in either direction. In heterogenous splitting, different split-fractions apply to each component. Lighter components can be separated from heavier components in separators where the fractions removed depend on the temperature and pressure applied. Heterogenous splitting requires one or more separation processes. Regulation of one process influences the outcome of the next, creating a system of non-linear relationships. Due to equipment characteristics such as high and low bounds on operating temperature for each separator, these functions are not continuous. In the model, heterogenous splitting is formulated as discrete choices between feasible split-fractions. Each set m 2 M R includes split-fractions akm i ; i 2 N for all components k 2 K, which express the ratio of each component to separate at the split node. Thus, for heterogenous splitting one need to select among jMj sets of split-fractions on all components. Eqs. (4)–(9) describe heterogenous splitting at a node i 2 NR where the first outflow goes to node j, and the second goes to node g. For each possible splitting m we define dummy variables wkm hi for
xkij
X
km akm i whi ¼ 0
8i 2 NR ; h ¼ f 1 ðiÞ;
m2M
j ¼ f1 ðiÞ; k 2 K; X
ð6Þ
m wkm 8i 2 NR ; hi chi ki 6 0
k2K
h ¼ f 1 ðiÞ; m 2 M; X
kmi ¼ 1
8i 2 NR ;
ð7Þ ð8Þ
m2M
kmi 2 f0; 1g 8i 2 NR ; m 2 M.
ð9Þ
Restriction (7) could have been formulated with upper capacity bounds on each component, but with varying flow composition it is difficult to get good bounds. Therefore, total flow capacity is used. Similar expressions as described above apply to homogenous splitting, but then the split-fraction is independent of component since the same fraction applies to all components. This could have been implemented by non-linear constraints, but to support the simple implementation with a few general building blocks and constraints, homogenous splitting was also formulated as a choice between sets of candidate split-fractions. 4.6. Market requirements The total flow to a sales node j 2 NS is limited by upper and lower bounds on demand, denoted by lj and uj respectively (10):
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lj 6
X
xkij 6 uj
8j 2 NS ; i ¼ f 1 ðjÞ.
ð10Þ
k2K
In addition, the quality of the flow must respect all quality requirements. Some quality requirements apply to groups of components, while others apply to single components. General quality restrictions for sales nodes are expressed by Eqs. (11) and (12). Here dkq is the weight for component k in quality measure q 2 Q, where Q is the set of all quality restrictions. The quality is restricted by a lower bound lijq and/or an upper bound uijq. Most quality restrictions apply to sales nodes, but similar restrictions can be specified for any network flow: X k X dq xkij lijq xkij P 0 8j 2 NS ; k2K
k2K
i¼f X k2K
1
ðjÞ; q 2 Q;
dkq xkij uijq
X
xkij 6 0
ð11Þ 8j 2 NS ;
k2K
i ¼ f 1 ðjÞ; q 2 Q.
products (13). To treat all products in all markets in a similar way, prices are expressed as unit prices, pkj , that may vary both with component k 2 K and market j 2 NS . Crude oil and NGL customers pay a weighted price dependent on the chemical composition of the product. This is modelled by letting the price pkj vary with k. Natural gas customers have such strict quality requirements that they pay per standard flow units delivered. Thus, pkj is independent of k in natural gas markets. For fixed splitting of oil and gas at platforms, the value of associated oil can be calculated as part of the pre-processing of data. This value depends on the oilÕs chemical composition and on the transport costs from the platform. The cost of producing from source t 2 T, adjusted for the value of oil, is denoted by xt. Production costs from different sources vary due to economies of scale and differences in production equipment: X X X X max z ¼ pkj xkij xt bt y t . ð13Þ i2N j2NS k2K
ð12Þ
Customers limit the energy content of the gas to ensure stable operating conditions in their processing plants and equipments. The energy content or gross calorific value (GCV) is equal to the weighted average of the potential energy of all components k 2 K. For this quality restriction q 2 Q, the dkq parameters in Eqs. (11) and (12) are equal to the potential chemical energy for each component k. The lower bound lijq and upper bound uijq, restrict minimum and maximum energy content. Customers also limit the relative content of single components such as carbon dioxide in the gas. High levels of carbon dioxide may cause erosion problems and some countries impose environmental taxes on emissions of the gas. In Eq. (12) this quality restriction q 2 Q has dkq ¼ 1 for k = carbon dioxide and dkq ¼ 0 for all other components. The maximum relative carbon dioxide content in the flow is limited by the upper bound uijq. There is no lower bound. 4.7. Objective function The model maximises the net income before taxes from the production and sale of petroleum
557
t2T
Fuel gas is consumed to transport gas to markets. As production of oil and NGL are limited by the demand for associated gas, Statoil could choose to maximise fuel gas consumption and thereby produce more oil and NGL. However, the government has regulated this condition by imposing a tax for fuel gas consumption. Fuel gas is sent to market nodes with negative prices equal to the taxes for fuel gas emissions. The compression work required to transport gas through a pipeline is a non-linear function of the gas flow. Consumption of fuel gas can be linearised within the range of permitted gas flow levels which is bounded by maximum gas flow capacity cij. As Fig. 5 shows, linearisation of the fuel gas consumption introduces errors, but this is considered acceptable as fuel gas consumption is less than 2% of the total gas production.
5. Implementation Database and reporting of results are implemented in a Visual Basic supported user interface in Excel. The software choice is based on plannerÕs preferences. The planner presses a macro-button in
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Fuel gas consumption
real model
Total flow Fig. 5. Real and approximated (model) fuel gas consumption in a compressor as a function of the gas flow.
the workbook to start XpressMP (Dash Associates, 2002) which reads input data, generates the matrix, optimises the problem and writes results back into the spreadsheet (see Fig. 6). Data are grouped in modules in the Excel workbook. The main module contains the most critical information and has links to all other modules. There are macro-buttons for navigating in the
database and for various data processing. All data processing operations are done in the spreadsheets. The model is formulated in the algebraic modelling language in XpressMP. The model can read data either directly from the spreadsheets or from .dat files automatically generated from the workbook. The latter alternative proved faster. Pre-processing of data supports a simple and generic model formulation and reduces the size of the matrix. For example, the number of variables is reduced by calculating the value of associated oil and NGL at platforms with fixed split and subtracting this value from the variable production costs, rather than modelling this as a fixed splitting node. Choices between discrete split-fractions are formulated by binary variables kmj and kkm j (see Section 4.5). The split-fractions can be sorted in a logic order for all splitting nodes. For homogenous splitting, they are simply sorted according to increasing fraction sent to the first successor node. For heterogenous splitting, it is a bit more complex. Here the order depends on both the fraction sent to the first successor node and on the rel-
1 Run optimisation
5 Write and present results in workbook
Excel workbook
Results files
4 Optimise and output solution
2 Write data to files
Model file
Matrix
3 Generate matrix
Fig. 6. Schematic representation of the optimisation process and the data handling involved.
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Troll
Åsgard A4 C B
39 49
29
Åsgard Transport
Statfjord Gullfaks
Kollsnes
48.1
Zeepipe IIA Heimdal
Statpipe
Condensate products
28.4
60
G TSSleipnerAH
Zeepipe IIB 31.6
11
R
9.7
Kårstø Statpipe E S Draupner Draupner Ekofisk
Europipe II 56.7
Dunkerque
Norpipe
Norfra
Zeepipe I Zeebrugge
18 Europipe I 23.8
Norsea
Netra
EMS
Optimal solution
39.5
22.3
21.7
42.4
47.1
Market demand
39.5
23.8
21.7
42.4
47.1
Fig. 7. Process flow sheet with results for the standard scenario. The oval nodes are platforms which collect flow from a number of connected wells. The lines are pipelines for transport to processing plants and to markets. The rectangles represent processing plants. The blank nodes are market nodes. Production figures are stated in million standard cubic metres per day [MSm3/d]. Figures in gray boxes report daily production of natural gas, while figures next to main pipelines report daily gas transport. The two bottom lines compare the gas sales to the market capacity in the five natural gas markets.
ative content of light components. As such ordering is possible, the binary splitting variables are coded as SOS1 sets (Beale and Tomlin, 1970). Thus, the optimisation process branches on splitting patterns as SOS1 sets. Post-processing data include visual presentation of main results in graphs and in a process flow sheet. Reading results into the results worksheets can be initiated automatically or manually by pressing a macro-button. Detailed results are presented in tables and aggregated results are shown in process flow diagrams as illustrated in Fig. 7.
production patterns are compared to a base case scenario. The base case represents the present network configuration and uses average daily demand data. The base case scenario has 756 continuous variables, 1197 columns, five binary variables, 10 semi-continuous variables, six SOS1 sets and 60 set members. The solution time on an Intel 4-M 1.7 GHz running WindowsXP was 4 minutes. Solution time is comparable for all scenarios. Solutions are presented in tables and process flow sheets. Fig. 7 shows an aggregate flow sheet with the solution for the standard scenario. We see that the model attempts to fulfil all demand for natural gas.
6. Results
6.1. Case 1: Fixed network configuration with demand variations
The model is solved for a number of different scenarios. The scenarios reflect changes in the network and in the demand situation. The suggested
Demand for natural gas varies during the year as consumersÕ need for heating or cooling changes.
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Natural gas production [MSm3/day]
Many consumers use gas directly for heating. For cooling, the gas is first transformed to electricity at gas power plants. To identify optimal production patterns for different demand levels, the model is solved for normal, high and low demand scenarios. Normal demand is equal to average yearly demand. High and low demand equals respectively 110% and 60% of average demand. Fig. 8 shows how natural gas production from fields vary for the three scenarios. The left graph shows total production output and the right graph shows output in percent of total capacity. The production output from an oil field equals the sum of production from wells connected to that field. The capacity of a field is limited by the production capacity from wells, processing capacities at the platform, and the gas pipeline capacity from the platform. In the high demand scenario, all fields except for the Troll and Ekofisk fields, produce at full capacity. When demand decreases, production is first reduced at these same platforms and in addition ˚ sgard. In the low demand scenario, producat A tion is also decreased at Heimdal and Sleipner. Limited demand for natural gas constrains production of associated oil and NGL. Therefore the model maximises production from fields with high rates of associated products. The StatGull field has the highest oil fractions and is therefore selected to produce at full capacity in all scenarios. Troll has low rates of associated oil and is used as a ‘‘swing’’-producer to handle most of the demand variations. Consequently, it has no production at low demand, but supplies 24% of total demand 70 60 50 40 30 20 10 0 Åsgard 60% demand
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in the high demand scenario. This general result corresponds to present operational policies for the Norwegian sector. 6.2. Case 2: Fixed demand and varying quality constraints For contract negotiations, it is necessary to know how the customerÕs quality requirements influence profit. To understand the effects of quality restrictions, the model was solved for a number of instances with different quality bounds. Results from changing bounds on the energy content (GCV) of sales gas are presented in Figs. 9 and 10. Here, the GCV bounds were simultaneously changed in the five natural gas market nodes. In each instance, the bounds were tightened or relaxed by a given percentage, relative to present quality restrictions. We assume that the price for natural gas is the same in each instance. The results in Fig. 9 show how total profit decreases with tighter quality requirements. Letters A, B, C and D in the figure refer to instances commented on in the following text. Fig. 9A shows the profit with present quality restrictions. When quality requirements are tightened by 1% (Fig. 9B), profit decreases, but this is not due to lower deliveries of gas. The system still fulfils nearly all natural gas demand (3.4% less in one market). The drop in profit is mostly due to lower output of oil and NGL products. This is because more of the energy-rich components are channelled into the natural gas to fulfil the Production in percent of total capacity
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Fig. 8. These graphs show variations in production output from main production platforms for different demand scenarios. The left graph displays total production output while the right graph displays production output in percent of total capacity.
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655 D Objective function value [MNOK/d]
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Fig. 9. Changes in the objective value as a function of the GCV quality requirements.
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Norsea
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Scenario C, 1.5% tighter GCV requirements
Fig. 10. Optimal GCV values for gas delivered in markets with different quality bounds in scenarios A and C.
GCV requirement. Further tightening of quality requirements, makes it infeasible to deliver natural gas in some markets. Then incomes from sales of both natural gas and associated oil and NGL decrease (Fig. 9C). Fig. 10 shows the GCV value of product delivered in five market nodes, for instances A and C from Fig. 9. In most cases, the optimal GCV value
for natural gas in the markets is close to the lower bound, as high energy components are more valuable if they are channelled into other products. The upper bound is only constraining if processing equipment cannot separate these components (Fig. 10C, Zeebrugge). This indicates possibilities to increase profit by installing better processing equipment.
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Also note that wider GCV bounds only give a slight improvement in profit (see Fig. 9D). This is because not much more of the energy-rich components can be extracted from the gas, with the existing processing equipment. Therefore the company should not pay for looser quality constraints. Also, customers should pay substantially more for higher quality gas. 6.3. Case 3: Contingency plans for system breakdown There are system breakdowns every year. The model can find new feasible and optimal production patterns to prepare for such breakdowns. At one point during the testing phase of the model, the workersÕ union threatened to go on strike and to close down the main gas production field, Troll, until their salaries were raised. This scenario was tested to see if new feasible solutions could be achieved. Unfortunately, Troll proved to be such an important gas producer, that some of the gas contracts could not be serviced. However, by using wells with low content of other petroleum products and more natural gas content, the remainder of the system was able to supply 96% of the demand. Fig. 11 shows how the production levels from wells change if Troll is closed.
7. Discussion and conclusion Simple building blocks with restrictive structures enable a generic and simple model formula-
tion. At the same time, the rigid structure increases the total number of nodes and flow variables. Fig. 12 illustrates how a direct formulation in (a), can be replaced by three standard blocks in (b), one collection block B, and two splitting blocks C. This increases the number of flow variables or arcs, but does not increase the number of split fractions, a1 and a2 versus b1 and b2. In the generic approach, there is one constraint for each building block type and combinations of these model the various real world processes. This greatly reduces the size of the model formulation compared to a more specific model. In a large and complex production system, this approach reduces the risk of errors in the formulation, and improves the ability to change the network by removing or adding pipes, nodes, sources or processing equipment. This functionality is an advantage in evaluating system breakdowns and possible system extensions. Planning tools for petroleum production can be divided into strategic, tactical and operational tools, according to their timeframe. Based on how they function, they can be further divided into optimisation and simulation based tools. Statoil uses an optimisation tool to support long term planning, similar to the one described by Nygreen et al. (1998), and are currently implementing an optimisation tool for detailed day-to-day planning. The model described here considers tactical planning and disruptions planning and is constructed to replace simulation based tools. Tactical planning consists of choosing a relatively stable production pattern to be maintained for some
Fig. 11. Production from 26 wells in one scenario with Troll producing at normal capacity (base case) and in the scenario with Troll closed due to a strike.
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(b)
(a)
B
C
α1
α2
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Fig. 12. Comparison between a specific modelling approach illustrated in (a) and a generic modelling approach illustrated in (b).
period of time, and disruption planning consist of identifying alternative ways to satisfy customers demand for shut-downs in parts of the system. In both cases, operators can limit the difference between the original and the new solution for production and splitting variables or add penalties on reduced sales. Still, the transition effort is often negligible in comparison to the benefit of using the optimal production pattern. Long term planning determines production regulation bounds that ensure long term optimality. Within these bounds, the tactical planning model will produce the most valuable petroleum first, and distribute petroleum components on products to maximise production of most valuable products. Assuming that all available petroleum resources will be exploited, less valuable petroleum will be used later. Thus, producing from sources with the most valuable petroleum first, only contributes to the long term profit by the depreciation of the higher value from these sources. The real value contribu-
tion from tactical planning comes from improving the way flow from the wells is processed and distributed on different products and markets. This requires careful planning of the processing and the regulation of production from sources to get the right quality. Tests showed that the total profit was strongly influenced by only small changes in quality requirements. This information is useful in contract negotiations to determine right prices for gas of different quality. Statoil suggested that the model could also be used to demonstrate the safety of stable deliveries to customers. If Statoil can demonstrate alternative ways to secure supply in case of a breakdown, this may increase customersÕ willingness to buy Norwegian gas. When the oil-workersÕ union threatened to close down production at the main gas production field, the model showed that by changing the production pattern, most demand could still be satisfied. This result demonstrates system robustness to customers.
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The main benefit of the model tool discussed here is the possibility to identify radically new ways to satisfy demand for varying network configurations. Alternatively this analysis is done by experts with profound knowledge of the network, checking the feasibility of new production patterns by combining results from several local simulation models. This is a cumbersome process which does not easily produce non-intuitive solutions. It is also hard to even identify feasible solutions without using optimisation, since most changes require very detailed adjustments across the system. The user interface improved communication with users both during the modelling process and after. Their possibility to access, understand and alter datainput supported the credibility of the model. Graphical presentation of results was in particular effective for communication with users that were not directly involved in the modelling process. References Beale, E.M.L., Tomlin, J.A., 1970. Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. In: Lawrence, J. (Ed.), Proceedings of the Fifth International Conference on Operational Research. Tavistock Publications, London, pp. 447–454. Bodington, C.E., Baker, T.E., 1990. A history of mathematical programming in the petroleum industry. Interfaces 20 (4), 117–127. Christiansen, M., Nygreen, B., 1993. Well management in the North Sea. Annals of Operations Research 43, 427– 441.
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