Linearized Pressure Drop Model for Gas Pipeline Capacity
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Solution Overview
Problem
Gas pipeline networks face challenges in maximizing capacity factor due to constraints on pressures, dynamic demand, and information asymmetry between operators and customers, making it difficult to simultaneously satisfy pressure constraints and maximize gas supply and demand effectively.
Innovation Solution
A system and method that uses a linearized pressure drop model and latent demand estimation to calculate network flow solutions, incorporating control elements and processors to manage flow and pressure, and employs machine learning models to determine hydraulic feasibility and latent demand, thereby optimizing gas flow and pressure management.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a nonlinear pressure drop model is used to accurately represent gas flow in pipeline networks, then measurement precision and hydraulic feasibility are improved, but device complexity and computational difficulty increase significantly
Solution Approach 1:
The patent transforms the nonlinear pressure drop relationship into a linear form by changing the parameter representation. Instead of using standard pressure (P), the system uses squared pressure (P²) as the parameter, which linearizes the pressure drop equation: P₁² - P₂² = K·Q². This parameter transformation maintains measurement precision while significantly reducing computational complexity and enabling the use of linear programming techniques for network optimization.
2Productivity
If the gas pipeline network operates at maximum capacity to increase productivity, then capacity factor is improved, but pressure constraints are violated and system reliability deteriorates
Solution Approach 1:
The patent implements a feedback mechanism where the linearized pressure drop model continuously monitors pressure constraints and provides feedback to the flow optimization process. The model calculates pressure drops based on actual flow rates and compares them against constraint limits, adjusting the optimization algorithm to ensure constraints are satisfied while maximizing capacity factor. This feedback loop enables the system to operate near maximum capacity without violating pressure constraints.
Solution Approach 2:
The system performs preliminary calculations using the linearized model to determine feasible flow rates before actual gas transmission begins. By pre-calculating the network flow solution that satisfies all pressure constraints and maximizes capacity factor, the system avoids operating in infeasible regions. This preliminary action ensures that when gas flows through the pipeline, pressure constraints are automatically satisfied while productivity is maximized.
3Adaptability or versatility
If real-time data collection and processing are implemented to improve adaptability to dynamic demand, then adaptability is improved, but loss of time for data processing and device complexity increase
Solution Approach 1:
The patent replaces complex iterative numerical optimization methods with a linear programming approach based on the linearized pressure drop model. This substitution transforms a computationally intensive nonlinear optimization problem into a more efficient linear programming problem that can be solved rapidly using standard algorithms. The linearized model allows the system to process real-time demand changes and recalculate optimal flow rates quickly, reducing data processing time while maintaining adaptability to dynamic conditions.
Data Source
AI summary
A system and method for controlling delivery of gas, including a gas pipeline network having at least one gas production plant, at least one gas receipt facility of a customer, a plurality of pipeline segments, and a plurality of control elements, one or more controllers, and one or more processors. The hydraulic feasibility of providing an increased flow rate of the gas to the gas receipt facility of the customer is determined using a linearized pressure drop model. A latent demand of the customer for the gas is estimated using a latent demand model. Based on the hydraulic feasibility and the latent demand, a new gas flow request rate from the customer is received. A network flow solution is calculated based on the new gas flow request rate. The network flow solution is associated with control element setpoints used by a controller to control one or more control elements.