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Unformatted text preview: PIPELINE ENGINEERING ALTERNATIVE PLANNING MODELS With the advance of mixed integer linear and non-linear programming methods, the optimization and planning of systems became more systematic. When intensive computations became viable, these planning models were extended to deal with data uncertainty through the so-called Two stage stochastic programming. We start presenting an ultra-simplified planning model, which should serve as basis for more complex and detailed models. In a later Module, design and optimization under uncertainty as well as risk management using these models are covered. We consider the case of a varying demand increasing in the future and we assume such demand will be covered. The time is discretized in several time periods (usually years) and what is needed to be determined is - Initial pipeline Capacity. It can be the demand in the first few periods, or the demand at the end of all periods. In the former case, expansions will be needed, while in the latter no expansions are needed and the pipeline will operate under- capacity for a period of time. - Expansions are to be achieved in some future period (to be determined) by adding a compressor at the middle point of the pipeline. This can be generalized to many compressors at many times and locations. Simplified Capacity Expansion Model SETS T: Time periods NT t ,..., 1 , = K: Compressor to be added/expanded. Compressors in parallel to be added to existing ones. VARIABLES Y kt : Expansion in period t takes place (Y t =1), does not take place (Y t =0) E kt : Expansion of capacity in period t. Addition of compressors Q t : Total pipeline capacity in period t. W t : Utilized capacity in period t. PARAMETERS sp t : Sales price in period t c t : Cost coefficient in period t (gas + operating costs). α t : Variable cost of expansion in period t β t : Fixed cost of expansion in period t Natural Gas Basic Engineering Copyright: Miguel Bagajewicz. No reproduction allowed without consent 2 L t : Discount factor for period t D t : Demand of gas for period t : , U kt L kt E E Lower and upper bounds on expansion in period t : max t CI Maximum capital available in period t : NEXP Maximum number of expansions MODEL EQUATIONS The objective function maximizes the net present value of the project. We try this linear objective first, although it is known that sometimes return of investment (ROI) is a better profitability measure. Moreover, under conditions where one can choose not to invest in unprofitable parts of the project, maximizing NPV is not equivalent to maximizing ROI and leads to different capital investments....
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- Spring '11
- Gas Basic Engineering