**3.4. Case study: Naphtha steam cracking model optimization**

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

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

An industrial multi-period steam cracking instance was used as a case study. Input data is shown in Table 4. The detailed feedstock composition was calculated using the Shannon entropy method [39]. An elementary reaction model and optimization with parallel simulation was used in this case study. The computer used in this optimization had eight cores of i7-2600 CPU and 4GB memory.

The optimization results show a 0.62% ethylene increase compared to the invariant operat‐ ing condition that was implemented in the practice. The comparison of the serial optimiza‐ tion results and optimization with parallel simulation results are shown in Figure 11 and Figure 12. It can be seen that the tendency of serial and parallel optimization results were the same. There was a high outlet temperature and high conversion of the major products in


the beginning and intermediate periods, and the outlet temperature of final periods were rather low for reducing the coke formation and for avoiding a high outer-wall temperature.

**Table 4.** Supporting information for the steam cracking optimization model.

The error of parallel simulation compared to serial simulation is shown in Table 5.

The CPU time of serial optimization was 17.78hr, while the CPU time of parallel optimization was 2.08hr. There was a 8.55 x speedup compared with serial optimization, because parallel calculation and a warm start strategy were used. Thus, the operating conditions could be dynamically optimized to track the changing market conditions.

The error in optimization with the parallel simulation model was caused by the surrogate coke thickness model. In eq. (22),

$$
\delta d\_t = d\_{t+1} - d\_t = f\left(t, \text{COT}\_t\right) \quad \forall t \in \{1, 2, \dots, N-1\} \tag{22}
$$

**Figure 11.** COT optimization results for serial and parallel simulation.

the beginning and intermediate periods, and the outlet temperature of final periods were rather low for reducing the coke formation and for avoiding a high outer-wall temperature.

PINA 0.3096 0.3223 0.2856 0.0825

*yC*2*H*4,*<sup>t</sup> <sup>o</sup>* <sup>+</sup> 0.48∑

*t*=1 10 *yC*3*H*6,*<sup>t</sup> <sup>o</sup>* )

ASTM (°C) 41.2 58.2 80.1 99.0 119.6 148.9 175.9

P I N A

IBP 10% 30% 50% 70% 90% EBP

**Feed**

**Operating condition**

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**Optimization variables**

Molecular weight 95.26 H/C 2.11

Feed rate (t/h) 5.4 Water/Oil (t/t) 0.54 Coil inlet temperature (°C) 636.5 Coil inlet pressure (Mpa) 0.31 Coil outlet pressure (Mpa) 0.04

Objective function max <sup>1</sup>

*NP* 8 *TM* (°C) 1000.0 *δ* (°C) 5.0 *LB* (°C) 855.0 *UB* (°C) 872.0

**Table 4.** Supporting information for the steam cracking optimization model.

dynamically optimized to track the changing market conditions.

Furnace runtime (day) 50

thickness model. In eq. (22),

d

<sup>10</sup> (0.52∑ *t*=1 10

The error of parallel simulation compared to serial simulation is shown in Table 5.

The CPU time of serial optimization was 17.78hr, while the CPU time of parallel optimization was 2.08hr. There was a 8.55 x speedup compared with serial optimization, because parallel calculation and a warm start strategy were used. Thus, the operating conditions could be

The error in optimization with the parallel simulation model was caused by the surrogate coke

*tt t d* <sup>+</sup><sup>1</sup> - *d* = *f* (*t Cd <sup>t</sup>* ) "*tO* Î= {1,, 2,L,*NT* - 1} (22)

**Figure 12.** C2H4 and C3H6 optimization results for serial and parallel calculation.

The feedstock composition and operating conditions, except COT, were fixed. However,

$$\delta d\_t = d\_{t+1} - d\_t = f\left(t, \text{COT}\_1, \text{COT}\_2, \dots, \text{COT}\_t\right) \quad \forall t \in \{1, 2, \dots, N-1\} \tag{23}$$

Accumulate coke thickness in each period was related to the operating conditions of all previous periods. Eq. (23) is simplified as eq. (22) to make the model easier to regress and the error caused by the simplification is acceptable according to the error shown in Table 5.


**Table 5.** Summarized optimization results for serial and parallel calculation.
