Yesterday I analyzed some of the considerations involved in modeling a section of a petrochemical refining process, namely that of hydrodesulfurization. That is adding hydrogen to hydrocarbons containing sulfur in the presence of a catalyst at an elevated temperature so the sulfhydryl (SH) groups can be split away and separated, to be replaced with the desired hydrogen atoms.
I examined an entire system and its larger context yesterday. Today I wanted to discuss a few more detailed considerations, with an eye toward the costs and benefits of taking different approaches. Bearing in mind that many variations of processes, reaction vessels, and equipment may be involved, and assuming we aren’t doing a finite-element solution where every container or vessel and every run of pipe is divided into multiple sub-volumes:
One Node vs. Many Nodes (or sub-volumes):
- Nature of materials and processes within the vessel: Many vessel models will contain single liquid and gas regions, but vessels with different types and arrangements of internal equipment may need to be represented individually.
- Presence of instrumentation or sampling ports at different locations along the vessel: Training simulators are all about the conditions and properties that operators can observe and affect. If multiple instruments or sample ports are located along the long dimension of a vessel the vessel may have to be subdivided into enough separate regions to provide unique results for the individual instrument or port locations. A change in feedstock composition, catalyst effectiveness, or hydrogen feed might provide indications that the reaction is completing (or failing to complete) at different locations.
- Amount of available computing power vs. need for model speed: Training simulators will theoretically need to run at or at least close to real time. If doing so is an issue then simplifications to the model may have to be made with respect to number of internal nodes or size of time step.
- Possible failure modes: The location of leaks or ability to specify reduced catalyst effectiveness at different locations may require specification of additional nodes.
Simultaneous vs. Non-Simultaneous Solution: The pressure-flow equations and possibly even the thermodynamic equations may be carried out using simultaneous solutions but the solution for transport properties might not be.
I once had to model a long coil of pipe in the offgas system of a nuclear power plant. The coil was located about halfway through the system after most of the liquid had been removed from the process flow. The purpose of the coil was to increase residence time so most of the short half-life radiation could decay. (I was told that this section of piping was buried outside under the parking lot, but that may or may not have been a joke.) I initially tried to model the transport of radiation using a simultaneous solution and found that non-zero concentrations showed up at the discharge end of the pipe the first time step after radiation was introduced at the charge end. The concentrations at the discharge end were small in magnitude but the character was wrong. This didn’t matter under steady state conditions but it would matter in a meaningful transient, and that was the whole point of the simulator.
I did the pressure-flow solution using the normal techniques (simultaneous matrix) but I decided to model the thermal and radiation transport (and decay) in the pipe coil as a series of ten rotating buckets, basically a bucket brigade, assuming roughly laminar flow. That meant averaging the radiation content of the inflow for one-tenth of the volume of the pipe and assuming that the radiation content at the discharge end was constant for that one-tenth of the pipe volume. (As I think about it I may have made a mistake by continuing to model radioactive decay as the discharge bucket emptied, which would have produced radiation levels that incorrectly sawtoothed over time. I’d have to think about how I should have handled that. As I think about it further I may also have been able to model the outgoing temperature as a constant equal to the ground temperature, if I had been desperate to save a few clock ticks.)
Perfect mixing is often a good enough assumption in simultaneously solved, one-dimensional fluid models but there are other times when it clearly won’t do. In those cases you may have to slow things down, do them by hand, or model them in a different way.