Pressure-Dependent Water Distribution Analysis Algorithm
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Solution Overview
Problem
Conventional water distribution models fail to accurately simulate and predict network behavior under pressure-dependent demand scenarios, such as during emergencies or pipe outages, as they assume constant demand values independent of pressure, leading to inaccurate flow calculations and criticality analyses.
Innovation Solution
A computer software program using a generalized, unified loop-node formulation and a novel global gradient algorithm to solve for unknown demands and junction pressures, allowing for the calculation of pressure-dependent demand and simultaneous solution of nodal heads and flows, thereby simulating scenarios where pressure affects water usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional water distribution models assume constant demand values independent of pressure, then the model formulation is simple and can be solved using traditional matrix techniques, but the model fails to accurately predict network behavior under pressure-dependent demand scenarios such as emergencies or pipe outages
Solution Approach 1:
The patent transforms the demand parameter from a constant value to a pressure-dependent variable. The demand at each node is expressed as a function of pressure head, allowing the model to adapt demand calculations based on actual pressure conditions in the network. This enables accurate prediction of demand under varying pressure scenarios while maintaining a systematic solution approach.
Solution Approach 2:
The patent introduces dynamic behavior into the demand calculation by making demand a function of pressure head rather than a static constant. The model dynamically adjusts demand values based on the pressure conditions at each node, allowing it to respond to changing system states such as pipe outages or emergency conditions where pressure varies throughout the network.
2Reliability
If pressure-dependent demand is incorporated into the model, then accurate prediction of network behavior under various pressure conditions is achieved, but the solution requires solving a more complex set of non-linear equations simultaneously
Solution Approach 1:
The patent combines the demand calculation and flow solution into a unified iterative process. Rather than solving demand and flow separately, the model simultaneously updates demand values based on pressure and solves the flow equations, merging what would otherwise be distinct calculation stages into a single integrated solution procedure.
Solution Approach 2:
The patent implements a feedback mechanism where pressure head values calculated from the flow solution are fed back into the demand calculation, which then updates the demand values for the next iteration. This feedback loop allows the model to progressively refine both pressure and demand values until convergence is achieved, ensuring accurate flow calculations under pressure-dependent conditions.
3Productivity
If demand is treated as a known constant value, then the hydraulic analysis can be performed using standard matrix techniques, but criticality analyses and asset management decisions become inaccurate under pressure-varying conditions
Solution Approach 1:
The patent performs preliminary calculations of pressure head distribution in the network before finalizing demand values. By first establishing the pressure field and then using those pressure values to determine demand, the model ensures that demand calculations are based on accurate pressure conditions, improving the reliability of subsequent criticality analyses and asset management decisions.
Data Source
AI summary
A computer software program provides an algorithm that solves for unknown demands (and junction pressures) within a modeling system that uses a generalized, unified loop-node formulation. The program can be used to calculate the available demand (i.e., the amount of water that is to be supplied) according to the nodal pressure. Both nodal heads and flows are simultaneously solved using a gradient algorithm, which allows, in accordance with the present invention, the model to simulate situations where a change in pressure affects the quantity of water used. Criticality analyses for segments of a system in such pressure dependent scenarios can also be performed using the software program of the present invention.