Tambin se han puesto a punto mtodos que amplan la regin de
convergencia utilizando tcnicas de continuacin, como en el caso de
Vickery-Taylor (1986), y que reciben el nombre de mtodos
homotpicos.
Homotopy continuation is applied to the industrially important
MTBE and methyl acetate reactive distillation (RD) columns to
analyse for steady state multiplicities. Continuation is applied in
two distinct ways, with respect to tray catalyst mass and with
respect to column inputs. Catalyst mass continuation provides a
tool for convergence to a steady state solution of the highly
non-linear governing equations. Also, the solution diagram reveals
the occurrence of multiple steady states. For the MTBE column, up
to five steady states in the kinetically controlled regime are
detected. Of these, only three remain in the limit of reaction
equilibrium on the trays. For the methyl acetate column, three
steady states in both the kinetically controlled and reaction
equilibrium regimes are obtained at fixed reflux rate and reboiler
duty. If the column specification is changed to fixed reflux ratio
and reboiler duty, only a single steady state solution is observed.
The column operating policy thus substantially impacts the
existence of multiple steady states. Column input continuation is
used to obtain the complex relationships between input variables
(reboiler duty, reflux rate, and so on) and output variables (tray
temperatures, conversion, and so on). Steady state multiplicities
are seen in both the MTBE and methyl acetate columns. A thorough
understanding of these multiplicities is essential for devising
robust control strategies. Steady state analysis of reactive
distillation using homotopy continuation - ResearchGate. Available
from:
http://www.researchgate.net/publication/231274878_Steady_state_analysis_of_reactive_distillation_using_homotopy_continuation
[accessed May 5, 2015].
Homotopy continuation applied to solving reactive distillation
MESH equations
A homotopy continuation method was developed for solving state
modelsof homogeneous conventional and reactive distillation with
typicalcolumn specifications. The equilibrium chemical reactions
are assumedto take place in the liquid phase, but the method is
also able toaccommodate vapour phase equilibrium reactions or to
include reactionkinetics through holdup or residence time. The
modified MESH equationsfor reactive distillation were formulated as
a problem-dependenthomotopy in such a way that the homotopy path to
a solution wascontinuous in the domain of interest, and that the
path seldom hasturning points. This allows the development of a
reasonable fast androbust solving method. 'Robust' here means that
the solution is foundwithout any need for manual iteration and any
initial guess given bythe user.
The method has been tested extensively for highly nonideal
ordinarydistillation. All the test cases for reactive distillation
show alsoglobal convergence characteristics. Performed studies on
the areamultiple steady states has further confirmed that the
method developedis reliable to produce a solution of the modified
MESH-equations. Therobustness of the method makes it possible to
use the MESH equationsat the early design phase: The search for
feasible state profiles forordinary and reactive distillation -
within the accuracy of the MESHequations - can be carried out
without interfering with the modelsolving procedure.
