Pipeline Network Pressure Estimation Across Operating States
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Solution Overview
Problem
The optimization of pipeline networks is hindered by their highly non-linear nature and the complexity introduced by binary variables and a large number of equations, leading to unsatisfactory results from conventional optimization methods like MINLP, especially over a distant time horizon.
Innovation Solution
A simulation method using three-dimensional dynamic matrices and weighting coefficients based on operating states to estimate pressure values in pipeline networks, reducing complexity and managing non-linearity by characterizing operating conditions with numerical parameters and discretizing time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional optimization methods like MINLP are used to handle binary variables and non-linearity, then the ability to make discrete decisions (start/stop equipment) is improved, but the calculation time becomes prohibitively long and results are unsatisfactory over distant time horizons
Solution Approach 1:
The patent segments the pipeline network into multiple zones based on topological characteristics and pressure boundaries. Each zone is modeled independently with its own mass balance equations, reducing the complexity of the overall system. This segmentation allows the use of simplified linear models within each zone while capturing the essential non-linear behavior at zone boundaries, thereby reducing calculation time while maintaining decision-making capability.
Solution Approach 2:
The patent transforms the non-linear pipeline network model into a linearized form by changing the mathematical parameters and variables used in the optimization. Specifically, it uses linear approximation techniques for pressure and flow relationships, and reformulates binary decisions as continuous variables with appropriate constraints, enabling the use of faster linear programming solvers while preserving the essential discrete decision-making capability.
2Device complexity
If a piecewise linear approach is used to replace non-linear equations, then the non-linearity management is improved, but the number of equations increases leading to prohibitive calculation time
Solution Approach 1:
The patent applies segmentation by dividing the pipeline network into zones rather than using piecewise linear approximation throughout the entire system. This zone-based segmentation reduces the number of equations needed compared to fine-grained piecewise linear methods, as each zone can be represented by a single set of mass balance equations with boundary conditions, maintaining calculation efficiency while managing non-linearity.
Solution Approach 2:
The patent applies partial linearization by linearizing only the essential relationships needed for optimization (mass balances and boundary conditions) while retaining non-linear characteristics where they most impact decision-making. This selective approach avoids the excessive equation generation of full piecewise linear methods while still managing non-linearity effectively.
3Measurement precision
If the pipeline network is modeled with a large number of equations to capture non-linear behavior accurately, then the accuracy of pressure estimation is improved, but the calculation time becomes prohibitively long
Solution Approach 1:
The patent segments the network into zones and applies mass balance equations at zone boundaries rather than detailed equations throughout the entire network. This reduces the total number of equations while maintaining pressure estimation accuracy at critical points (nodes and boundaries), achieving a balance between accuracy and computational efficiency.
Solution Approach 2:
The patent uses simplified linear models as copies or approximations of the full non-linear system for the purpose of optimization and real-time control. These linearized zone models replicate the essential behavior of the non-linear system sufficiently for decision-making, avoiding the need to solve the complete non-linear system while maintaining adequate accuracy for operational purposes.
Data Source
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AI summary
The present invention concerns a simulation method and a system (1) for the management of a pipeline network (PN) comprising input and output nodes (S1, S2, C1). The simulation method comprises: - defining operating states characterizing operating conditions of the pipeline network, - determining, for each operating state STp, a three-dimensional dynamic matrix DMSTp whose each coefficient DMSTp(i,j,tk) corresponds to a pressure variation value from an initial pressure value at a j-th node at a k-th time step tk following a variation, at a i-th node, of a flow rate value, - estimating, for a given node at a given moment, a pressure value on the basis of an operating schedule providing information regarding variations of the flow rate value for each node and evolutions of the operating conditions of the pipeline network until said given moment, said estimation using the operating states and the three-dimensional dynamic matrices.