Pipeline Network Pressure Estimation Using 3D Dynamic Matrices
Find Innovative SolutionsGenerate Solutions
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, and excessive calculation time.
Innovation Solution
A simulation method that defines operating states and uses three-dimensional dynamic matrices to estimate pressure variations, allowing for the management of non-linearity by characterizing operating conditions and weighting coefficients based on a numerical parameter, reducing the complexity of the system and improving estimation accuracy.
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 excessively 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 hydraulic behavior. Each zone is modeled independently with its own dynamic matrix, reducing the overall computational complexity. This segmentation allows the system to handle binary decisions locally without requiring full-network optimization calculations, thereby reducing calculation time while maintaining decision-making capability.
Solution Approach 2:
The patent transforms the non-linear hydraulic equations into linearized forms by changing parameters - specifically by using dynamic matrices that represent incremental changes in pressure and flow rather than absolute values. This parameter transformation allows conventional linear optimization methods to be used instead of computationally intensive non-linear methods like MINLP, significantly reducing calculation time while preserving the essential decision-making functionality.
2Measurement precision
If a large number of equations are used to accurately describe the non-linear pipeline network, then the accuracy of the optimization results is improved, but the computational complexity and calculation time increase prohibitively
Solution Approach 1:
The patent changes the parameters from absolute pressure and flow values to incremental dynamic matrices representing small changes around operating points. This transformation linearizes the non-linear hydraulic equations, allowing accurate results to be obtained through sequential linear optimization steps rather than requiring a single complex non-linear model with prohibitively many equations.
Solution Approach 2:
By dividing the pipeline network into smaller zones, the patent reduces the number of equations needed for each local optimization problem. The global accuracy is maintained through the coordination of multiple local zone models, where boundary conditions are adjusted iteratively until convergence is achieved across the entire network.
3Ease of manufacture
If piecewise linear approach is used to replace non-linear equations, then the non-linearity problem is addressed, but the number of equations increases rather than being limited
Solution Approach 1:
Instead of using piecewise linear approximation which multiplies the number of equations, the patent changes parameters to dynamic matrices that directly represent the linearized relationship between pressure and flow changes. This single matrix-based approach achieves the same linearization goal without fragmenting the model into multiple piecewise segments, thereby avoiding the equation multiplication problem.
Data Source
AI summary
A simulation method for the management of a pipeline network having input and output nodes (S1, S2, C1) and including defining operating states describing operating conditions of the pipeline network, determining, for each operating state STp, a three-dimensional dynamic matrix DMST<sub2>p </sub2>whose each coefficient DMST<sub2>p</sub2>(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, and 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 the given moment, the estimation using the operating states and the three-dimensional dynamic matrices.