Gas Pipeline Network Flow Control with Linearized Pressure Drop
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Solution Overview
Problem
Current methods for controlling gas pipeline networks struggle with efficiently calculating network flow solutions that satisfy energy consumption constraints and pressure constraints, often resulting in stranded molecules and venting of industrial gas due to the complexity of nonlinear pressure drop relationships and the difficulty in solving nonconvex optimization programs.
Innovation Solution
A system and method that calculate minimum and maximum production rates at industrial gas production plants to set bounds on production rates, linearize the nonlinear pressure drop relationship within these bounds, and use these models to determine network flow solutions that satisfy energy consumption, pressure, and demand constraints, with error bounding to ensure accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If nonlinear pressure drop relationships are used to calculate network flow solutions, then accuracy of pressure constraints is improved, but computational complexity and difficulty of solving nonconvex optimization programs increases
Solution Approach 1:
The patent transforms the nonlinear pressure drop relationship into a linear form by changing the parameter representation. Specifically, it uses a linear pressure drop model where pressure drop is expressed as a linear function of flow rate within bounded regions, converting the nonconvex optimization problem into a convex linear programming problem that is computationally tractable while maintaining sufficient accuracy for network flow solutions.
2Productivity
If linear pressure drop model is used to simplify calculations, then computational efficiency is improved, but accuracy of pressure constraint satisfaction deteriorates
Solution Approach 1:
The patent divides the network flow calculation into multiple iterations, with each iteration solving a linear programming subproblem. The solution from one iteration becomes the basis for the next, progressively refining the flow solution. This segmented approach allows the use of computationally efficient linear models while converging toward a solution that satisfies the original nonlinear pressure constraints.
Solution Approach 2:
The patent implements an iterative feedback mechanism where the linear pressure drop model is used to generate initial flow solutions, which then inform updated flow bounds for subsequent iterations. The feedback loop continuously refines the solution by adjusting flow bounds based on previous iteration results, ensuring that pressure constraints are progressively satisfied while maintaining computational efficiency.
3Ease of operation
If flow bounds are calculated using network bisection method, then ease of calculation is improved, but risk of stranded molecules and venting increases
Solution Approach 1:
The patent performs preliminary calculations to establish initial flow bounds using the network bisection method before executing the main iterative algorithm. These preliminary bounds serve as a starting point that guides the subsequent iterative refinement process, ensuring that the algorithm begins with feasible flow directions and progressively improves the solution to prevent stranded molecules and venting.
Data Source
AI summary
Controlling flow of gas in a gas pipeline network, wherein flow of gas within each of the pipeline segments is associated with a direction (positive or negative). Processors calculate minimum and maximum production rates (bounds) at the gas production plant to satisfy an energy consumption constraint over a period of time. The production rate bounds are used to calculate minimum and maximum signed flow rates (bounds) for each pipeline segment. A nonlinear pressure drop relationship is linearized to create a linear pressure drop model for each pipeline segment. A network flow solution is calculated, using the linear pressure drop model, comprising flow rates for each pipeline segment to satisfy demand constraints and pressures for each of a plurality of network nodes over the period of time to satisfy pressure constraints. The network flow solution is associated with control element setpoints used to control one or more control elements.