(509e) Time-Scales in Distillation Models

Promatch is a European project and has as its objective plant-wide control or control of large-scale processes such as glass ovens for which CFD models are easily in the order of million of states for a reasonably accurate description of the process. The Promatch subnet, consisting of RWTH Aachen with W Marquardt and the control company Cybernetics in Trondheim together with this group at NTNU has chosen to exercise model reduction on a Norwegian gas plant located in Korstø. A second pro-ject having the same feel is the Mongstad Pilot project, in which we are looking into improving the ecology of this largest Norwegian refinery. In both projects distillation is the dominating processing units besides utilities such as heat exchangers. In both cases one is interested on the high-level description of the process aiming at plant-wide operations and both projects have recently been started and the two subgroups are collaborating on understanding the dynamics of distillation columns and the gen-eration of low-dimensional nonlinear dynamic approximation of columns and their associated components.

The chosen first object of our study is the C4-splitter for which we have already mod-els and industrial experiences. Statoil's research centre has performed intensive stud-ies of the column and its immediate environment with the aim of implementing Model Predictive Controllers but found that the linear techniques are not sufficiently good for achieving the desired performance. Dynamic experiments of the type step distur-bance on the various manipulatable inputs have indicated surprisingly consistent dy-namics and highly nonlinear gains, which immediately generates a demand for simple nonlinear models.

Current activities

Dynamic Flash

The first step was to look into the model of the column. The aim was to implement it in the modeling tool MODELLER (Preisig, 2004), which initially failed triggering work on the core element of the model, namely the dynamic flash. Static flash calculations are a crucial part in simulations of distillation column dynam-ics. Solving the steady state flash equations, which are part of the dynamic distillation model often leads to numerical convergence problems. Therefore the flash calcula-tions are the bottleneck in the dynamic distillation column simulation.

Traditional approaches for solving the flash calculations are based on partial steady state assumptions, which lead to the convergence problems (Moe, 1996). To over-come these problems Preisig (2004) proposed to use a physical description of the flash model based on Lewis' two-film theory, which has good convergence proper-ties. The proposed approach may also be advantageous in case of fast input changes or high frequency disturbances, since the steady state assumption is not valid in this case.

A paper by Preisig and Westerweele (2003) documents the results of first going in the opposite direction, namely to refine the description rather than lump it, which would be model reduction. In this case we looked at the basic physical process in more detail and formulate the flash as a two phase system with dynamic heat and mass transfer between the phases. Taking into consideration the relative dynamics of the two trans-fer processes, it is well known that the heat transfer process, being based on momen-tum transfer on the molecular level is faster than the mass transfer, where molecules have to move relative to each other. Taking into consideration those facts, one can proof sequential conversion first of the temperature and second of the mass distribu-tion between the two phases. This eliminates the need for the initialization of the standard model, which has this time-scale assumptions built in, so-to-speak, assuming event dynamics for the two types of transfers and negligible capacity of the gas phase.

Our first work is to construct column models based on this dynamic description and let the DAE solver take care of stiffness problem that arises from modeling the gas-phase as a dynamic system. Accuracy of the solution and dynamics of the solving al-gorithm, in particular the time to find a solution compared to simulating a ?standard? model will be reported.

In addition we are going to show the insufficiency of using steady state flash equa-tions related to fast input changes or high frequency disturbances.

Hydraulics

The change of the internal flows is on a very short time scale as the columns are es-sentially adiabatic and the heat input in the boiler and the withdrawal in the cooler are fast. It is expected, though, that the change of the hold up is significantly slower and one of the main sources of the observed dynamics as they were observed in the plant. The currently steady-state hydraulics of the plant will be modeled as a dynamic sys-tem and its dynamics will be compared with the dynamics of the internal streams as they change with changing heat input and output. We expect that this will explain the observed transition dynamics. If we can construct reduced-order models is not in the books as yet.

Model reduction methods

We are currently exploring methods that go beyond the classical quasi-steady-state assumption. Specifically, higher-order approximations to the slow manifold in the systems are sought, which also take into account slowly varying inputs to the system. This then results in a band of slow manifolds whereby the applicable solution is se-lected based on the excitation dynamics.

Citations

Moe, H.I.: 1996, Dynamic process simulation: studies on modelling and index reduc-tion, PhD thesis, Norwegian University of Science and Technology, Trondheim, Norway.

Preisig, H.A.: 2004, Computer-aided modelling: a study on the dynamic flash, Inter-nal Report PSE 2004.009, Norwegian University of Science and Technology, Trond-heim, Norway.

Preisig, H A, Westerweele, M R: 2003, Effect of Time-Scale Assumptions on Process Models and Their Reconciliation; ESCAPE 13, Lappeenranta, Finnland.