Abstract
We present a decision support tool for tactical planning in the natural gas supply chain. Our perspective is that of a large producer with a portfolio of production fields. The tool takes a global view of the supply chain, including elements such as production fields, booking of transportation capacity, bilateral contracts and spot markets. The bilateral contracts are typically take-or-pay contracts where the buyer’s nomination and the prices are uncertain parameters. Also the spot prices in the market nodes are uncertain. To handle the uncertain parameters, the tool is based on stochastic programming. The goal for the producer is to prioritize production over the planning period in a way that makes sure that both delivery obligations are satisfied and that profits are maximized. The flexibility provided by the short-term markets gives the producer a possibility to further increase his profits. Production and transportation booking decisions in the early periods are taken under the uncertainty of the coming obligations and prices which makes flexible and robust solutions important. There will be a trade-off between maximum profits and robustness with respect to delivery in long-term contracts.
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Abbreviations
- \(\mathcal {N}\) :
-
The nodes in the transportation network
- \(\mathcal {B}\) :
-
Booking nodes, \(\mathcal{B} \subseteq \mathcal{N}\)
- \(\mathcal {G}\) :
-
Production fields, \(\mathcal{G} \subseteq \mathcal{B}\)
- \(\mathcal {D}\) :
-
Delivery nodes for the contracts, \(\mathcal{D} \subseteq \mathcal{B}\)
- \(\mathcal {M}\) :
-
Spot markets in the network, \(\mathcal{M} \subseteq \mathcal{B}\) and \(\mathcal{M}\cap \mathcal{D}=\emptyset\)
- \(\mathcal{I}(n)\) :
-
Nodes with outflow going to node n
- \(\mathcal{O}(n)\) :
-
Nodes with inflow coming from node n
- \(\mathcal {C}\) :
-
The contracts in the portfolio
- \(\mathcal{C}^\mathrm{split}\) :
-
Contracts in the portfolio with multiple delivery nodes, \(\mathcal{C}^\mathrm{split} \subseteq \mathcal{C}\)
- \(\mathcal{C}(d)\) :
-
The contracts in delivery node d, \(\mathcal{C}(d) \subseteq \mathcal{C}\)
- \(\mathcal{D}(c)\) :
-
The delivery nodes of contract c, \(\mathcal{D}(c) \subseteq \mathcal{D}\)
- \(\mathcal {Y}\) :
-
The years included in the optimization horizon
- \(\mathcal {T}\) :
-
The time periods in the optimization horizon
- \(\mathcal{T}^\mathrm{booking}\) :
-
The time periods where booking decisions can be made
- \(\mathcal{T}(y)\) :
-
The time periods included in year y
- \(\mathcal {S}\) :
-
The scenarios
- \(\mathcal {Z}\) :
-
Event nodes in the scenario tree
- \(\mathcal{S}(z)\) :
-
Scenarios passing through event node z
- K g :
-
The unit cost for production in field g
- H b :
-
The per unit tariff in booking node b
- X bt :
-
Booked firm capacity in booking node b for transportation in time t
- A bt :
-
Volume available for booking in node b for transportation in time t
- Q m :
-
The maximum trade in spot market m, time t and scenario s
- \(C^{\max}_{cd}\) :
-
The maximum fraction of nominated gas in contract c that can be delivered in delivery node d
- \(C^{\min}_{cd}\) :
-
The minimum fraction of nominated gas in contract c that can be delivered in delivery node d
- γ c :
-
The fraction of gas that can be sourced freely for delivery in contract c
- F ij :
-
The flow capacity between the downstream nodes i and j
- \(\overline{F}_{gt}\) :
-
The maximum daily production in field g and time t (aggregated to match period length)
- \(\underline{F}_{gt}\) :
-
The maximum daily production in field g and time t (aggregated to match period length)
- \(F^\mathrm{year}_{gt}\) :
-
The maximum yearly production in field g and year y
- T z :
-
The time period of event node z
- \(P_{\textit{mts}}^\textrm{spot}\) :
-
The spot price in market m in time t in scenario s
- \(P_{\textit{cts}}^\textrm{contr}\) :
-
The price in contract c in time t in scenario s
- \(V_{\textit{cts}}\) :
-
The demand in take-or-pay contract c in time t in scenario s
- \(\pi_{\textit{ts}}\) :
-
The probability of scenario s
- \(k_{\textit{gts}}\) :
-
Production in field g in time t in scenario s
- \(q_{\textit{mts}}\) :
-
Spot sale in time t in scenario s. Negative values represent purchase
- \(v_{\textit{cdts}}\) :
-
Volume delivered in take-or-pay contract c in delivery node d in time t in scenario s
- \(v_{\textit{cdts}}^\mathrm{eq}\) :
-
Equity gas delivered in split contract c in delivery node d in time t in scenario s
- \(a_{b \tau\textit{ts}}\) :
-
The balance of transportation capacity booked from booking node i to booking node j at time τ for transportation in time t in scenario s
- \(h_{b\tau\textit{ts}}\) :
-
The booking of transportation capacity from booking node i to booking node j in time τ for transportation in time t in scenario s
- \(f_{\textit{ijts}}\) :
-
Flow from nodes i to node j in time t and scenario s
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Acknowledgments
This project has been supported by Statoil and the Research Council of Norway (project number 144217/212), for which we are grateful.
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Fodstad, M., Midthun, K.T., Rømo, F., Tomasgard, A. (2011). Tactical Portfolio Planning in the Natural Gas Supply Chain. In: Bertocchi, M., Consigli, G., Dempster, M. (eds) Stochastic Optimization Methods in Finance and Energy. International Series in Operations Research & Management Science, vol 163. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9586-5_11
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