# Oil Supply Chain Planning under Uncertainty and Risk Evaluation Marcelo Maia F. de Oliveira October 15th, 2014.

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Oil Supply Chain Planning under Uncertainty and Risk Evaluation Marcelo Maia F. de Oliveira October 15th, 2014

1.Introduction and Problem Definition Wide variety of comercial, industrial and logistics operations occur over the midstream segment Strong dependence among the operations and some gains can only be estimated by considering the whole supply chain Planning this segment is crucial to achieve the success of all operations.

2.Oil Supply Chain in Brazil 3 4 5 6 1 2 Curde Oil: - Imports (1) - Exports (3) - Production (5) Oil Products: - Imports (2) - Exports (4) - Market Selling (6) ~ 200 different crude oils ~ 50 different oil products 10 basins of oil production 43 terminals (marine and inside the country) 12 refineries

3.Refinery Operations There are two main operations executed in the refineries: Process UnitsBlending Units types: Physical Separation – Disttilation (first step of oil processing) Conversion – Cracking and Delayed Coker (residual oil and heavy fractions to gasoline and diesel) Treating – HDT Naf and HDT Diesel (remove impurities – sulfur – and specify other qualities) Blendin types: 1 – Oil blending aiming to generated intermediates with desired yields and qualities; 2– Intermediate blending to specify charge of process unities; 3 – Intermediate blending to produce final products with specified qualities.

The two-stage stochastic problem (Higle, 2005) can be described as presented by the equations: e x ≥ 0 e y ≥ 0 x is the first stage variable. Its value must be determined before the uncertainty ω is unfold. y is the second stage variable. Its value is decided after the uncertainty ω is fully known. 4. Bibliographic Review: Stochastic Programming Solution well posicioned in respect with the possible realizations of uncertainty ω. Second stage decisions in a posicion to explore advantageable values of uncertainty ω. Where &

4. Bibliographic Review: Scenario Generation Methods Moment Matching – Statiscal Method proposed by Hoyland e Wallace (2001) which applies a non-linear model to generate a limited number of dicrete scenarios that satisfy specific statistic properties. Time Agregation – sampling method that uses Markov Chain concepts (Ergodic Chains, Return Time and Mean Path Lenght) and the Time Agregation method of Cao et al., 2002.

The CVaR of a probability distribution with confidence level α: Mean value of those scenarios which have the profits lower than VaR and whose cumulative probability sums up to 1- α (Pineda e Conejo, 2009) 4. Bibliographic Review: Cvar - Risk Measure

Oil Production Brent QuotationOil Products National Market 5.Uncertainties of Oil Supply Chain in Brazil Uncertainty taken as the prediction error The value of each uncertain parameter is based on the same 54 months period 3 parameters combined + de 150 thounsand possible realizations

First Stage Second Stage Month 1Month 2 Oil import and export Decisions: Oil allocation, Spot market oil import and export, unit utilization, oil products import and export. 6.Mathematical Model and Problem Approach

First Stage Constraints: 1.Global Oil Balance (import+ production = export + allocated); 2.Oil Import and Export Limits; Second Stage Constraints – scenario dependent: 1.Global Oil Balance

6.Mathematical Model and Problem Approach – Recourse actions Predicted Production – Actual Production Production Surplus Spot Market Export Allocation in refineries Production Deficit Export Cancellation Allocation Cancellation Besides these options, it’s also possible to import oil in the Spot Market. Second Stage Global Oil Balance:

6.Mathematical Model and Problem Approach First Stage Constraints: 1.Global Oil Balance (import+ production = export + allocated); 2.Oil Import and Export Limits; Second Stage Constraints – scenario dependent: 1.Global Oil Balance 2.Oil Product Balance (import+ production = export + processed); 3.Oil and Product Balance on Terminals; 4.Products Market Selling; 5.Flow of oil and product limited to the deciosions of importation, exportation, production and selling.

6.Mathematical Model and Problem Approach Second Stage Constraints – scenario dependent - Refinery Operations: 1.Intermediates balance (produced by process unit= product blending + charge blending); 2.Charge Balance (charge blending = consumed by process units); 3.Oil Products Quality Specification; 4.Charge Quality Specification; 5.Process Unit Capacity Limits; 6.Storage Limits; 7.Oil Product Balance (produced by blending + initial storage + received = delivered + final storage). Intermediate qualities indexed to avoid non- linearity

6.Mathematical Model and Problem Approach Objective Function:

7.Model Parameters: Products Crude OilTypeOrigin A1CondensateImported A2CondensateNational B1Extra-LightImported B2Extra-LightNational C1LightImported C2LightNational D1Crackable ResidueImported D2Crackable ResidueNational E1MediumImported E2MediumNational F1HeavyNational G1Extra-HeavyImported G2Extra-HeavyImported Derivados GLP Naphta Gasoline Kerosene Diesel 10 Diesel 500 Fuel Oil Coke Crude Oil ListOil Product List

12 refineries in the country Shared oil supply systems, distribution of oil products and market influence area 4 refineries (each one with a different complexity) 7. Model Parameters: Refineries

Nodes: International Market (IM), National Production (PN), Terminal (Tn) and Refineries (4 Rn) 7 arcs: 1 for Import, 1 for Export, 1 for National Production e 4 for Oil Supply to Refineries R1 R2 R4 R3 T1 IM PN MN 7. Model Parameters: Oil Logistics Operations

Nodes: International Market (IM), Terminal (Tn), Refineries (4 Rn) e National Market (MI) 14 arcs: 1 for Import, 1 for Export, 16 for flows between refineries and terminal e 4 for market delivery R1 R2 R4 R3 T1 IM PN MN 7. Model Parameters: Oil Products Logistics Operations

7. Model Parameters: Refineries

1.Process Units: a.Distillation; b.Cracking (FCC); c.Delayed Coker; d.HDT Diesel; e.HDT naphta. 25 x 47 Matrix of oil and intermediates converted to intermediates 2.Blending: a.47 x 8 matrix of intermediates to oil products; b.Quality Specification: sulfur (Gasoline, Diesel e Fuel Oil), octane (Gasoline) e viscosity (Fuel Oil) 7. Model Parameters: Refineries

7.How does the uncertainty affect the scenario profit? Linear influence of Oil Production – the higher the production, more oil is exported. Smoother influence of Quotation, as both import costs and export revenue varie. The higher the demand, the bigger the supply cost, as internal prices are lower than international ones.

8.Results – Scenario Generation Methods Moment Matching Method Cumulative Probability Curve for oil production uncertainty Time Agregation Method Moment Matching Method  high concentration of Probability in narrow range of the possible values. Time Agregation Method  uniformity and curves overlapped.

8.Results – Scenario Generation Parameter Selection 1- Gain on objective function stability as the scenario tree grows, mainly for the Moment Matching Method.

8.Results – Objective Function and Scenario Profit (thousand u.m.) ReplicationMoment Matching Time Agregation 121.16021.045 221.16820.967 321.13521.103 421.16821.108 521.16221.112 Mean 21.15921.067 Stand. Deviation 1462 Moment MatchingTime Agregation

Replication Revenue (K u.m.) Products Sale Oil Export Product Export 135.75170.3%22.4%7.3% 235.62169.9%22.7%7.4% 335.46770.5%22.2%7.3% 435.65070.2%22.7%7.1% 535.61569.9%22.7%7.4% Moment MatchingTime Agregation 1- Similartity of each cost and revenue quotas 2- Time Agregation Method: higher product exchange – higher cost and revenue 8.Results – Revenue and cost Replication Revenue (K u.m.) Products Sale Oil Export Product Export 136.57369.6%22.2%8.2% 236.26769.3%22.5%8.2% 336.57369.4%22.3%8.3% 436.47370.1%22.0%8.0% 536.22169.5%22.3%8.3% Replication Total Cost (K u.m.) Oil Import Product Import Refining Cost Logistic Cost 114.61460.4%29.2%6.1%4.3% 214.45160.7%28.7%6.2%4.4% 314.36960.0%29.4%6.2%4.4% 414.67160.8%28.7%6.1%4.3% 514.44260.9%28.6%6.2%4.3% Replication Total Cost (K u.m.) Oil Import Product Import Refining Cost Logistic Cost 115.63556.7%33.4%5.7%4.1% 215.41758.0%32.1%5.8%4.1% 315.53157.2%32.9%5.8%4.1% 415.45856.9%33.2%5.8%4.1% 515.23557.9%32.1%5.9%4.1%

8.Results – First Stage Variables PeriodOil12345 Month 1A115.090 B1892 7141.700893 E139.698 G13.0382.9401.7682.7493.076 Month 2B13.1833.2663.2993.9553.200 E115.98912.87513.35213.36013.084 G14.5426.9506.0696.0606.834 Period Oil 12345 Month 1D217.89017.79317.30317.97217.844 E234.82135.52834.55035.83335.629 Month 2D217.43917.79317.30317.946 Moment MatchingTime Agregation 1- High resemblance in first stage indications: 2- Oil A1 Import (low price and good yield) until the limit; 3- Oil D2 e E2 Export until the limit respecting the second stage uncertainties. Import (thousand m³) Export (thousand m³) PeriodOil12345 Month 1A115.090 B1656620890656626 E139.698 G11.6601.6961.6651.6601.690 Month 2B13.109 E114.20913.75915.05516.09714.628 G15.1305.5804.2843.2424.710 PeriodOil12345 Month 1D217.539 E234.291 34.53034.291 Month 2D217.174 Import (thousand m³) Export (thousand m³)

8.Results – Second Stage Recourse Actions Moment Matching 1- Strong indication of allocation adjustment as oil production deficit happens. 2- The oil export decision is generally kept on the second stage. Agregação temporal MonthA2B2C2D2E2F1G2 1Deficit (K m³)62950251500203603 % Scenario97% % Allocation Canc.100% 94%95%100% 2Deficit (K m³)62950251500203603 % Scenarios97% % Allocation Canc.100% 95%100% MonthA2B2C2D2E2F1G2 1Deficit (K m³)188113969913965661683 % Scenario60% % Allocation Canc.100% 83%96%100% 2Deficit (K m³)188113969913965661683 % Scenarios60% % Allocation Canc.100% 97%100%

8.Results – Disttilation utilization Moment MatchingTime Agregation 1 – Maximum utilization of disttilation on R3 and R4 - robust indication; 2 – Maximum utilization of distillation on R2 doesn’t seem to be interesting on the second month; 3 – Lower utilization on R1 for solutions using Time Agregation Method.

8.Results – Product Qualities GasolineDiesel 10Diesel 500Fuel Oil MethodMonthRefinery OctaneSulfur Viscosity MomentMonth1R1 100%0%100%0%100% Matching R2 100%0%100%0%100%81% R3 100%0%100%0%100% R4 100%0%100%0%100% Month2R1 100%0%100%0% 100% R2 100%0%100%0%100% R3 100%0%100%0%18%100% R4 100%0%100%0% 100% TimeMonth1R1 100%0%100%0%100% Agregation R2 100%0%100%0%100%57% R3 100%0%100%0%100% R4 100%0%100%0%100% Month2R1 100%0%100%0%8%100% R2 100%0%100%0%99%100% R3 100%0%100%0%19%100% R4 100%0%100%0%6%100%

8.Results – Risk Measure Impact(CVaR) Moment MatchingTime Agregation 1- Clear difference of the risk measure on the Objective Function for each generation method; 2- Scenario trees built by the moment matching method are less susceptible to risk and the Objetive Function varies only when changing the risk aversion (β).

8.Results – Risk Measure Impact on Scenario Profit Moment Matching Replication 2 Time Agregation Replication 2 1- ↑ Risk Aversion (β) e ↑ Confidence Level (α) : to avoid low values of profits, the curve moves to the left, so higher profits are also avoided. 2- Confidence Level (α) effect on the solutions obtained by Time Agregation Method: desirable for decision taking in an uncertain environment.

9.Conclusions 1.The instance built for this problem, even though simplified, reflect the complexity of oil supply chain planning; 2.The results obtained are suitable for real operations and give some important insights of how to deal with the uncertain factors considered; 3.Compairing the results obtained by both scenario generation methods allows to identify qualities and disadvantages of each one; 4.It was clear that the Time Agregation Method has a more desirable behaviour in function of risk measures parameters; 5.The problem here present could be closer do real operations, considering the integer nature of oil and product import and export operations or by taking into account other sources of uncertainty, such as asset availability; 6.Other mathematical techniques could be applied, for example Lagragian Decomposition, which would drive to a smaller computational effort.

Contact marcellomaia@gmail.com maiamarcelo@petrobras.com.br

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