(672e) The Effects of Kinetic and Hydrocarbon Distribution on the Multiplicities of Deep Hydrodesulfurization Via Catalytic Distillation

Reactive
distillation was first proposed by Backhaus (1921); since then, various
processes have been proposed, and
nowadays, it is becoming an important unit operation. A reactive distillation
column integrates the reaction and separation in a single unit which makes its
open loop behavior complex. Kienle and Marquardt (2002) classified its
open-loop behavior as:  i) processes with
equilibrium-controlled/fractionation-controlled chemical reactions; ii)
processes with kinetically controlled reactions, where all components have
similar boiling points; and iii) kinetically controlled processes with large
boiling point differences. Any of these may result in multiplicities and
complex attracting sets.  The physical mechanisms leading to
multiplicities are different. Various efforts have been made to explain the
multiplicities in these systems. For non-reactive distillation columns,
multiplicities may arise as a result of:  i) singularities in the
mass-molar relationship, ii) the presence of an azeotrope, or iii) the
dependence of the heat of vaporization on composition for certain input
variables.  However, a reactive distillation column is more complex, since
chemical reactions take place and there are more operating and design variables
that may cause multiplicities. In this system, the chemical reaction may
produce a rapid change in the product composition without requiring a change in
the feed-split or the energy balance (Chen et al. 2002). Thus, it is important
to identify the region where a reactive column operates to detect possible
operation problems from the design stage.

In this work,
the effects of kinetic and hydrocarbon distribution on the multiplicities of a
light gas oil (LGO) deep hydrodesulfurization (DHDS) two-bed catalytic
distillation column (CDC) are studied. The physical mechanisms leading to
multiplicities are identified and the multiplicity region is found for the
reflux rate (RR) and bottom flow rate (B). These
are the main operating variables and are generally used as control inputs. The
Damköhler number (Da), which is the ratio of the
characteristic residence time to the characteristic reaction time, is used to
identify the mechanism leading to multiplicities. When Da > 1
the system is equilibrium-controlled/fractionation controlled, while when Da
< 1 the system is kinetically controlled.  The CDC
studied in this work has 14 stages and two reactive zones. LGO is fed between
the reactive sections while hydrogen is fed below the second reactive section.  

To identify the
multiplicity region and to evaluate the effect of the hydrocarbon distribution
on the multiplicities, three hydrocarbon mixtures are used. The first is a real
LGO fraction which is modeled as pseudocompounds; the second is a synthetic gas
oil mixture (SGO), while the third is a lighter synthetic gas oil mixture
(LSGO). The multiplicity regions for the CDC described above, for the three
hydrocarbon mixtures, are identified and the bifurcation plots of the reflux
rate (RR) and bottom flow rate (B) as a function of
the Da number are presented.

The
fractionating effects are clearly shown by the RR(Da)
plots where double limit singularities are observed for the LGO. The
multiplicity regions for the lighter mixtures (SGO and LSGO) are smaller than
the multiplicities of the heavier mixture (LGO). For the LGO mixture, up to
five multiplicities are found, while for the SGO and the LSGO mixtures only
three steady states are observed. On the other hand, the B(Da)
plots show a rich multiplicity behavior where up to seven multiplicity regions
are found for the SGO mixture, while four multiplicity regions were found for
the LGO fraction. Isola branches, 0/∞-disjoint, double limit
singularities, and the classical S-shape multiplicities were found for both the
LGO and SGO mixtures. Disjoint bifurcations result in non-feasible
operating regions that separate non-closed disconnected steady-state solution
branches. This behavior arises when there are bounds on the values of the
parameters or state variables. Determining the feasible operating region is
important during the design of feedback control.

Results show
that this is an equilibrium-controlled/fractionation controlled chemical
reactions system. This is, multiple solutions may be present for design and
operating conditions that approach reaction equilibrium (Da > 1).
Yet, a unique solution is expected at low Da numbers. In this system, the H₂
must be dissolved in the liquid phase so the reaction takes place. Yet, if the
temperature decreases, the hydrogen diluted in the liquid phase increases.
However, when the reaction section temperature decreases, the reaction rate
also decreases.  Here, the inverse correlation of these phenomena is
clear. Therefore, we conclude that the multiplicities are the result of
equilibrium-driven self-inhibition phenomena, which are the result of the
presence of dissolved H₂ in the mixture. Results also show that the
hydrocarbon distribution plays an important role in the occurrence of
multiplicities. The hydrocarbon distribution in the mixture modifies the
activity coefficients and thus, the boiling point of the mixture. This affects
the internal heating/cooling flows and the reaction rates. In addition, it is
shown that for RR(Da), the multiplicity region is
reduced for the lighter hydrocarbon mixtures, while for B(Da)
it increases. It is also shown that the column operating point lies in a unique
solution region that is far away from the multiplicity region. Yet,
multiplicities may pose a problem during the start-up operations.

References

[1] A.A. Backhaus, (1921). Continuous processes for the manufacture
of esters, US patent 1400849.    [2] F. Chen, R.S. Huss,
M.F. Doherty, M.F. Malone, Multiple Steady States in Reactive Distillation:
Kinetic Effects, Computer and Chemical Engineering, 26 (2002) 81-93.
   [3] A. Kienle, W. Marquardt (2002), Nonlinear Dynamics and
Control of Reactive Distillation Processes. In K. Sundmacher and A. Kienle
(Eds), Reactive Distillation-Status and Future Directions, Wiley-VCH:Weinheim,
241-281.