Equation-of-State Pseudo-Density Root for Real-Time Process Control
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Solution Overview
Problem
Existing thermodynamic modeling and simulation systems face challenges in achieving timely and consistent convergence to a thermodynamic state solution, leading to difficulties in real-time plant control due to heavy processing demands and inefficient algorithms.
Innovation Solution
The method involves determining pseudo-properties over a dynamically determined range of an independent variable using specific extrapolation equations and departure points in the thermodynamic equation of state, promoting improved computational efficiency and consistent convergence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If iterative calculations of complex thermodynamic equations are performed to accurately describe dynamic situations, then manufacturing precision is improved, but productivity deteriorates due to heavy processing loads
Solution Approach 1:
The patent transforms the complex iterative thermodynamic equations into non-iterative algebraic equations by changing the mathematical parameters and formulation approach. This allows direct calculation of thermodynamic properties without repeated iterations, maintaining accuracy while dramatically improving computation speed for real-time control applications
Solution Approach 2:
The patent replaces the iterative computational mechanism with a direct algebraic solution mechanism. By substituting the iterative calculation system with a closed-form algebraic approach, the system achieves both accuracy and real-time processing capability without the computational burden of repeated iterations
2Reliability
If constant updating of thermodynamic models is performed to keep models current, then reliability is improved, but loss of time increases due to heavy processing demands
Solution Approach 1:
The patent changes the computational parameters from iterative numerical methods to direct algebraic solutions, enabling rapid recalculation of thermodynamic states as conditions change. This allows continuous updating of predictive models without the time penalty of iterative computations, maintaining reliability while reducing computation time
3Ease of operation
If complex thermodynamic equations are solved in real-time for plant control, then ease of operation is improved, but productivity deteriorates due to CPU processing demands
Solution Approach 1:
The patent substitutes the iterative computational system with a direct algebraic calculation system, enabling real-time thermodynamic modeling without overwhelming CPU resources. This substitution maintains full real-time control capability while preserving processing throughput for other plant operations
Data Source
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AI summary
A thermodynamic modeling system comprising a computer, a thermodynamic process simulation application, and a thermodynamic equation of state application is provided. The thermodynamic equation of state application determines a density root based on a first and second point of departure from an equation of state and based on a first and a second extrapolation equation. The first departure point satisfies the equation the partial derivative of pressure with respect to density equals a first constant times the pressure divided by the density plus a second constant. The density root is determined as a pseudo-density in a phase two when the specified pressure is greater than the second departure point pressure and in a phase one when the specified pressure is less than the first departure point pressure. The thermodynamic process simulation application invokes the thermodynamic equation of state application to determine a result based on the density root.