Differential-Algebraic Approach to Dynamic Simulations of Flash Drums with Rigorous Evaluation of Physical Properties

Abstract

Résumé -Simulation dynamique de séparateurs de mélanges liquide-vapeur avec une approche différentielle algébrique et évaluation rigoureuse des propriétés physiques -La dynamique de séparateurs de mélanges liquide-vapeur est simulé avec des propriétés physiques rigoureusement calculées en utilisant une équation d'état pour modéliser chaque phase. La formulation fournit un ensemble d'équations différentielles algébriques (DAE), dont les équations différentielles décrivent les bilans matérielles et énergétiques et les équations algébriques décrivent les conditions d'équilibre à l'intérieur du séparateur. PSIDE (Parallel Software for Implicit Differential Equations) [Lioen et al., 1998] est utilisé pour résoudre l'ensemble des DAE avec efficacité. Dans cette approche, les équations sont résolues simultanément, avec des itérations directes de température, de volumes de phase et de nombre de moles de chaque composant dans chaque phase. Les résultats montrent l'efficacité de cette méthode de simulation des séparateurs de mélanges liquide-vapeur. [Lioen et al., 1998] Abstract -Differential-Algebraic Approach to Dynamic Simulations of Flash Drums with Rigorous Evaluation of Physical Properties -The dynamics of flash drums is simulated with rigorous physical properties calculations using an equation of state to model each phase present. The formulation results in a set of differential-algebraic equations (DAE), whose differential equations describe the material and energy balances and the algebraic equations result from the conditions for thermodynamic equilibrium inside the drum. PSIDE (Parallel Software for Implicit Differential Equations)

Two-Phase Flow in Pipes: Numerical Improvements and Qualitative Analysis for a Refining Process

“…This approach is expected to prove more efficient in that all differential equations and algebraic constraints will be simultaneously processed, instead of sequentially being iterated for in a nested structure. CPU-cost gains are typical benefits of not separately solving algebraic equations in every step, as verified by [17] in a flash-drum DAE problem.…”

Dynamic simulation of fluids in vessels via entropy maximization

“…Direct entropy maximization, however, was not the solution method adopted in most recent papers that deal with the UVn flash problem and use EOS [11][12][13][14]. Direct entropy maximization has been avoided as the method to solve UVn flash problems mostly because the thermodynamic properties derived from the equations of state commonly used for chemical process design are explicit functions of temperature, volume, and number of moles, but not of internal energy.…”

“…Because the volume of the vessel is known, the state of the fluid inside the vessel corresponds to the solution of a UVn flash. It is possible, for example, to solve an isothermal flash (specified TPn) in the inner loop and update temperature and pressure in the outer loop until matching the internal energy and volume specifications, or use other nested [11,13] or single [12,14] loop approaches. Furthermore, there are several possible ways of writing the phase equilibrium equations.…”

“…The equilibrium condition corresponds to the saddle point of the mathematical function that results from such reformulation. Lima et al [14] followed this reformulation [12] of the algebraic equations but used a solver capable of handling high-index DAE problems directly (PSIDE) [15]. These papers [11,12,14] discuss examples with at most two phases.…”

“…Lima et al [14] followed this reformulation [12] of the algebraic equations but used a solver capable of handling high-index DAE problems directly (PSIDE) [15]. These papers [11,12,14] discuss examples with at most two phases. gPROMS, a commercial software, can simulate vessel dynamics with phases modeled by equations of state using its interface with Infochem's Multiflash program, but implementation details are scarce in the open literature.…”