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.