Gas Pipeline Network Flow Control Using Linearized Pressure Models
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current methods for calculating network flow solutions in gas pipeline networks are inefficient due to the complexity of nonlinear equations, leading to difficulties in satisfying pressure constraints and resulting in stranded molecules and venting of industrial gases.
Innovation Solution
A system and method that calculate minimum and maximum signed flow rates for each pipeline segment using a network bisection method, linearize the nonlinear pressure drop relationship, and use a linear program to ensure pressure constraints are met, incorporating error bounds to account for inaccuracies in the linearization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If nonlinear equations are used to calculate network flow solutions, then accuracy of pressure predictions is improved, but calculation efficiency deteriorates
Solution Approach 1:
The patent transforms the nonlinear pressure drop equations into linear form by changing the mathematical parameters and variables (e.g., using squared pressure terms and linear flow terms). This linearization maintains sufficient accuracy for practical applications while enabling the use of efficient linear programming algorithms, thus resolving the contradiction between accuracy and computational efficiency.
2Productivity
If linear approximation is used for pressure drop relationship, then calculation speed is improved, but pressure prediction accuracy deteriorates
Solution Approach 1:
The patent uses carefully selected linear approximation parameters based on typical operating conditions and physical properties of gas flow. By transforming the nonlinear relationship into a linear form with appropriately calibrated coefficients, the method achieves both computational speed and sufficient engineering accuracy.
3Adaptability or versatility
If minimum and maximum flow rates are not bounded, then flexibility in network operation is improved, but reliability of pressure constraint satisfaction deteriorates
Solution Approach 1:
The patent performs preliminary calculations to determine minimum and maximum flow rate bounds for each pipeline segment before solving the network flow problem. These pre-established bounds are then incorporated into the linear programming constraints, ensuring that pressure requirements are satisfied while maintaining operational flexibility within the determined ranges.
Data Source
AI summary
Controlling flow of gas in a gas pipeline network, wherein flow within each pipeline segment is associated with a direction (positive or negative). Minimum and maximum signed flow rates are calculated for each pipeline segment constituting lower and upper bounds, respectively, for flow in each pipeline segment. A nonlinear pressure drop relationship is linearized within the lower and upper flow bounds to create a linear pressure drop model for each pipeline segment. A network flow solution is calculated, using the linear pressure drop model, and includes flow rates for each pipeline segment to satisfy demand constraints and pressures for each of a plurality of network nodes to satisfy pressure constraints. Lower and upper bounds on the pressure constraint comprise a minimum delivery pressure and a maximum operating pressure, respectively. The network flow solution is associated with control element setpoints used by a controller to control one or more control elements.