**a.** Feedstock composition prediction

applied to the operating condition optimization problem to obtain a more reliable optimization result. Based on this, a surrogate coke thickness model is proposed to make multi-period

The general idea of this chapter is outlined in Figure 1. The first step in the conceptual development of a detailed molecule-based model for a complex feedstock is to determine an accurate molecular representation of the feedstock. Then, a multi-scale steam cracking model is established following the feedstock prediction. Finally, operating condition optimization of

multi-period steam cracking is carried out using the established multi-scale model.

**Figure 1.** Diagram of simulation and optimization of the steam cracking process methodology

**2. Steam cracking model**

**2.1. Multi-scale model for steam cracking**

are presented and discussed. Finally, section 4 offers conclusions from this study.

This chapter is structured as follows. Section 2 offers a detailed discussion of the establishment of the multi-scale steam cracking model; a case study for naphtha steam cracking simulation is presented. Section 3 provides the operating condition optimization model; surrogate coke thickness model and parallel simulation are used to accelerate the computing of the optimi‐ zation model. A case study of operating condition optimization is presented and the results

A multi-scale model is proposed in this chapter to reveal the nature of the steam cracking process and to generate a reliable and robust model for accurately predicting the yields of

optimization with parallel simulation possible.

120 Advances in Petrochemicals

Conventional analytical techniques are generally incapable of directly measuring the identities of all the molecules in complex feedstock, especially for the high carbon number range; however, this applies only to indirect characteristics [37]. Here, the Shannon entropy method [38] and probability density function were used to predict detailed feedstock composition, based on the analytical data. A detailed model for feedstock composition prediction can be found in [39]. The objective function of this NLP (non-linear programming) problem is shown in eq. (2), where *S(x)* is Shannon entropy and *xi* is the mole fraction of component *i*.

$$\max S(\mathbf{x}) = -\sum\_{i=1}^{n} \mathbf{x}\_i \ln \mathbf{x}\_i \tag{2}$$

Figure 2 shows the predicted feedstock composition using Shannon entropy, compared with the experimental data. The predicted results show the effectiveness of the Shannon entropy theory in obtaining the missing information for models of the steam cracking process.

### **b.** Process-level model

A process-level model consists of mass balance equations, momentum balance equation and energy balance equation (eqs. (3-5)) [40, 41]. For the simulation of smooth tubular reactor types, the use of a one-dimensional reactor plug-flow model is generally recognized as providing a sufficient degree of accuracy, as all radical profiles are wiped out due to the high turbulence corresponding to Reynolds numbers of over 250 000. The plug-flow reactor model implicitly assumes that there is no mixing in the axial direction, but rather, perfect mixing in the transverse direction [2].

$$\frac{dN\_m}{dL} = \frac{S}{V} \sum\_i \nu\_{i,m} r\_i = f\_N\left(T, P, N\_m\right) \tag{3}$$

$$\frac{dP}{dL} = -\frac{f \cdot E(L) \cdot G^2}{5.07 \times \rho \cdot D\_i \times 10^4} = f\_P \left( T, P, N\_m \right) \tag{4}$$

$$\frac{dT}{dL} = \frac{k\pi D\_o(T\_w - T) - \sum\_m \Delta H\_{fm}^0 \cdot \frac{dN\_m}{dL}}{\sum\_m c\_{pw} N\_m} = f\_T \left( T, P, N\_m \right) \tag{5}$$

In eq. (3), *Nm* is the concentration of species *m* and *L* is the length of the reactor tube. *S* is the flow area, *V* is the volume flow rate, *μim* is the stoichiometric coefficient of reaction *i* and *ri* is the reaction rate of reaction *i*. In eq. (4), *P* is the pressure of the mass flow, *f* is the Fanning friction factor, *E(L)=Le/L*, *Le* is the equivalent length of the reactor tube, *G* is the mass flow rate, *Di* is the internal diameter of the tube and *ρ* is the density of the gas mixture. In eq. (5), *T* is the temperature of the mass flow, *Do* is the outer diameter of the tube, *k* is the overall heat transfer coefficient, *Tw* is the outer wall temperature of the tube, *ΔHfm0* is the standard heat of formation of species *m* and *cpm* is the specific heat of species *m*.

It should be noted that the measuring point of the COT (coil-outlet temperature) of an industrial furnace is usually on the outer wall of the tube. Thus, the measured COT has a temperature difference from the outlet temperature of the gas mixture. Eq. (6) has been derived from heat balance equations in order to adjust to the temperature difference; the results show that there exists a 15-20K temperature difference, which agrees well with what has previously been reported.

$$\Delta \text{COT} = \frac{\lambda\_{\text{Isolation}} \left( \text{COT} - T\_{\text{isolation}\_{\text{-}o}} \right)}{\ln \frac{r\_o + d\_{\text{isolation}}}{r\_o}} \left( \ln \frac{r\_i}{r\_i - d\_{\text{coke}}} + \frac{\ln \frac{r\_o}{r\_i}}{\lambda\_{\text{nale}}} + \frac{1}{\alpha\_{\text{uniform}} (r\_i - d\_{\text{coke}})} \right) \tag{6}$$

In eq. (6), *λisolation* is the heat transfer coefficient of the isolation layer. *Tisolation\_o* is the outer wall temperature of the isolation layer, *ro* is the external diameter of the tube, *ri* is the interior diameter of the tube, *disolation* is the thickness of isolation layer, *dcoke* is the thickness of coke and *αmixture* is the heat transfer coefficient of the gas mixture in the tube.
