Algebro-differential Equation Simulation for Chemical Process Modeling
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Solution Overview
Problem
Current methods for simulating chemical or biochemical processes in fine chemicals and biotechnology industries are either too simplistic, limiting the number of scenarios, or overly complex, requiring numerous physico-chemical parameters, making them impractical for quick and accurate predictions, especially in the early stages of process development where resources are limited.
Innovation Solution
A system and method that combines algebraic and differential equations, allowing for the conversion of explicit algebraic equations into algebro-differential equations, enabling the integration of both types of equations into a single simulation system, which can simulate complex scenarios with reduced requirements for physico-chemical parameters, and allows users to choose between fine-grained or simplified modeling based on the operation's importance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If detailed modeling methods (e.g., Honeywell UNISIM®, Aspen HYSYS®) are used to achieve precise simulation, then manufacturing precision is improved, but device complexity increases due to the large number of physicochemical parameters required
Solution Approach 1:
The patent segments the simulation model into two distinct types: algebraic equations for operations where internal state is unknown or unnecessary, and differential equations for operations where internal state is known and dynamics matter. This segmentation allows each type to be applied appropriately, avoiding the need to use complex differential equation models for all operations, thereby reducing overall model complexity while maintaining precision where needed.
Solution Approach 2:
The patent applies partial modeling by selecting only the necessary level of detail for each operation. For operations where internal state variables are unknown or not critical, simple algebraic equations are used instead of full differential equations. This partial application of detailed modeling reduces the number of parameters required while maintaining sufficient simulation precision for the specific application context.
2Ease of operation
If empirical knowledge methods are used to simplify the simulation process, then ease of operation is improved, but manufacturing precision deteriorates due to limited scenarios and inability to predict dynamics
Solution Approach 1:
The patent introduces dynamics into the simulation by incorporating differential equations that can model transient behavior and time-dependent processes. This allows the system to predict dynamics and transient regimes, overcoming the static limitation of empirical methods while maintaining relative simplicity through the structured two-type equation approach.
Solution Approach 2:
The patent changes the mathematical parameters and models used in simulation from purely empirical relationships to a hybrid system incorporating both algebraic equations and differential equations. This parameter change enables the model to capture dynamic behavior and improve accuracy while remaining operable through clear classification rules for selecting between equation types.
3Manufacturing precision
If comprehensive detailed modeling is used to capture all process operations, then manufacturing precision is improved, but loss of time increases due to the complexity of determining numerous parameters
Solution Approach 1:
The patent segments the modeling approach into two categories with different parameter requirements. By classifying operations into those suitable for algebraic equations and those requiring differential equations, the system avoids determining numerous physicochemical parameters for operations where simple algebraic relationships suffice, thereby reducing the time required for parameter determination while maintaining accuracy where it matters.
Solution Approach 2:
The patent applies partial detailed modeling by using comprehensive differential equation models only for operations where internal state is known and dynamics are critical. For other operations, simpler algebraic equations are used, avoiding the excessive time investment required to determine all the physicochemical parameters that would be needed for full detailed modeling of every operation.
4Device complexity
If simple algebraic equation methods are used to reduce complexity, then device complexity is reduced, but manufacturing precision deteriorates because transient regimes and dynamics are not taken into account
Solution Approach 1:
The patent incorporates dynamics by introducing differential equations that can model transient behavior, time-dependent processes, and internal state evolution. This allows the system to capture dynamic effects that simple algebraic equations miss, improving simulation accuracy for operations where dynamics matter, while maintaining simplicity through the structured approach of using algebraic equations where appropriate.
Data Source
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AI summary
The present invention relates to a system for the computer simulation of a chemical process comprising at least one first operation described by an explicit algebraic equation, said system comprising a receiving module for receiving the first explicit algebraic equation, a processing module configured to transform said explicit algebraic equation into an algebro-differential equation and a solving module configured for solving the algebro-differential equation.