**3.3. Optimization with parallel simulation**

*t tt t* ( ) *i i*

= = å å (21)

 , = =

*t t d f t COd T* 1 1 d

**Figure 6.** Optimization procedure with multi-period steam cracking simulation.

and the surface is from surrogate model.

in period *t* can be regressed using the polynomial function shown as eq. (20). Here,

the coke thickness data is generated using the original multi-period simulation model and based on this, a surrogate coke thickness model is obtained through regression. The coke thickness using the surrogate model and original multi-period simulation model are shown in Figure 7. Dots in Figure 7 are coke thickness from the original multi-period simulation model

The coke thickness from the surrogate model fits well with the original model; thus, the decoupled multi-period cracking model, combined with the surrogate coke thickness model was used in the multi-period simulation. The initial coke distribution along the serial operation periods was carried out using the surrogate model. Thus, the multi-period simulation problem was decoupled into *N* sub-problems and simulated, respectively, in parallel, as shown in

Thus, *δd<sup>t</sup>*

132 Advances in Petrochemicals

Figure 8.

Figure 8 shows optimization with a parallel simulation procedure using the surrogate coke thickness model.

**Figure 7.** Coke thickness from the surrogate model and original multi-period model.

In Figure 8, a surrogate coke thickness model is regressed from the results of the original multiperiod model and the surrogate coke thickness model generates the coke thickness distribution for each period prior to the simulation. Once the surrogate model is regressed, the process for each period can be simulated in parallel. The simulation results are sent to the optimization model. If the criteria are satisfied, the optimization stops; if not, the optimization model generates a new set of COT and returns it to the simulation model.

There are several common types of parallel computing methods: phase parallel, divide and conquer parallel, pipeline parallel, master-slave parallel and work pool parallel methods. In this instance, the work pool parallel job partitioning method was used in the optimization. Simulation for one period can be treated as one job in the parallel simulation. All the jobs are stored in the work pool; processors fetch jobs from the work pool as long as the work pool is not empty. A detailed scheme for parallel simulation is shown in Figure 9.

In Figure 9, *NP* is the resources that can be used in a parallel simulation (*NP*=computer number×processor number for each computer) and *NJ* is the period number in the multi-period simulation. If *NP≥NJ*, that means all jobs can be calculated in one iteration. Otherwise, *NP* jobs

**Figure 8.** Optimization using a parallel simulation procedure.

**Figure 9.** Detailed scheme for parallel simulation.

must be fetched from the work pool and be postponed until all processors are idle before the next iteration. Simulation will continue until the work pool is empty.

Another benefit of using parallel simulation is a warm start. To accelerate the steam cracking simulation, iteration information is stored after the first simulation, which is called a warm start. If the iteration information is recorded, it can be used as an initial value in the next simulation for reducing CPU time. A comparison between a warm start for serial and parallel simulation is shown in Figure 10.

**Figure 10.** Comparison between a warm start for serial and parallel simulation, based on the multi-period steam crack‐ ing model.

Iteration information for the most recent period is stored in serial simulation. The iteration information for each period is not entirely the same. Inconsistency of iteration information makes the simulation slow. In a parallel simulation, however, iteration information for each period can be stored. This delivers a faster simulation for each period.
