Example of PackedColumn model

[emima94]

Hi,

I am new to IDAES and I want to build a simple, dynamic model for a solvent-based absorber/desorber system using the PackedColumn unit. But it is not fully clear to me how to set it up correctly. Does anyone have an example of a model using the PackedColumn unit?

Thx!

/Emil.

[dallan-keylogic]

Unfortunately, there's no such thing as a "simple" dynamic model for a solvent-based absorber/desorber system. The present PackedColumn model is not set up for dynamics. In order to add system holdup, you'll need to add DistributedVars.variant cross-sectional area terms to the vapor_phase and liquid_phase, then write a constraint that those cross-sectional areas sum up to the columns overall cross sectional area (probably modified to remove area occupied by the packing---I think they use the real velocity, not the superficial velocity, but I'm not 100% sure). Then you need to set up some sort of pressure-driven flow in the vapor phase (and if you somehow have flow-reversal in the vapor phase, then the ControlVolume1D will probably break down.)

Even with those changes implemented, you may end up with a high-index DAE (see this paper for a good introduction to DAE index reduction). These absorber/desorber systems use reactive solvents, which results in equilibrium relationships between species concentrations. If material balances are written for these "true species" compositions (like what is done in the MEA column example), there is then an algebraic relationship between "differential" variable initial conditions. In order to reduce the DAE index, some of those "differential" variables need to be converted into "algebraic" variables, which can be done in Pyomo by deactivating the discretization equations for those variables. However, you need to provide additional equations in order to replace those equations. You typically get those new equations by differentiating existing equations, but these equations typically contain new variables, so more equations need to be differentiated until you end up with a square system. There is an algorithm that can tell you which equations you need to differentiate, but it hasn't been implemented in IDAES. You can often get away with adding fewer equations by performing this procedure by hand and setting certain small nonzero values to zero.

A much easier method would be to write material balances based on the "apparent" species in the system. For the MEA-CO2-H2O system, MEA, CO2, and H2O are the "apparent" species, while H2O, MEA, CO2, MEAH^+, MEACOO^-, and HCO3- are the "true" species (here we're assuming that the concentrations of OH^- and CO3^2- are small enough to ignore). Another alternative is converting the speciation equations from equilibrium reactions to rate reactions, then using an arbitrarily large kinetic constant. You'd then need to use that rate reaction model in every model in the absorber/desorber system and you'd end up with a very stiff system of equations.

We want to create some additional tutorials explaining this issue of elevated DAE index at some point in the near future.