Convergence of block boundary value methods for solving delay differential algebraic equations with index-1 and index-2

2021 ◽  
Vol 399 ◽  
pp. 126034
Author(s):  
Jingjun Zhao ◽  
Xingzhou Jiang ◽  
Yang Xu
Keyword(s):  
Boundary Value ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Boundary Value Methods ◽  
Block Boundary ◽  
Index 2 ◽  
Delay Differential

scholarly journals Biodiesel Production by Reactive Flash: A Numerical Simulation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Alejandro Regalado-Méndez ◽  
Sigurd Skogestad ◽  
Reyna Natividad ◽  
Rubí Romero
Keyword(s):  
Numerical Simulation ◽  
Differential Algebraic Equations ◽  
Biodiesel Production ◽  
Algebraic Equations ◽  
Flow Ratio ◽  
Bubble Point ◽  
Biodiesel Quality ◽  
Index 2 ◽  
Globally Stable ◽  
System Approaches

Reactive flash (RF) in biodiesel production has been studied in order to investigate steady-state multiplicities, singularities, and effect of biodiesel quality when the RF system approaches to bubble point. The RF was modeled by an index-2 system of differential algebraic equations, the vapor split (ϕ) was computed by modified Rachford-Rice equation and modified Raoult’s law computed bubble point, and the continuation analysis was tracked on MATCONT. Results of this study show the existence of turning points, leading to a unique bubble point manifold,(xBiodiesel,T)=(0.46,478.41 K), which is a globally stable flashing operation. Also, the results of the simulation in MATLAB® of the dynamic behavior of the RF show that conversion of triglycerides reaches 97% for a residence time of 5.8 minutes and a methanol to triglyceride molar flow ratio of 5 : 1.

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