The Mathematical Model of FCC Feed Optimization

The mathematical formulation of the FCC feed optimization is as follows (BP Amoco Group, 1991). Altogether, it consists of three different objectives to be maximized and is subjected to four constraints. The details of the derivation for these equations are complex and will not be revealed as it is considered a trade secret by the organization. 

Maximize Fmx, which consists of certain ratio of the waxy feed and feeds with low specific density. This combination is to reduce the viscosity and thus reduce the flash-point of the waxy feed so that the reaction process will consume less energy. 

Maximize Dif the differentiated total flows of F6 and F7. The complexity here is due to the very heavy viscosity of these feeds. Reaction process will be slow when viscosity is high. However with the right temperature it will overcome this constraint. Thus 

Maximize Fmi, which is related to a ratio of FI, F4 and Dt. FI feed is high in sulfur that will form acid gas, which causes serious corrosion of pipes and extremely hazardous to people when inhaled. By optimizing this formula the unconverted oil of F4 and Dt will reduce the acidity in some way and make it feasible for the reaction to take place at the same time. 

The range of the individual feed volumetric flow rate as shown in Table 9.1. 

---

The mathematical model of FCC feed optimization described in section 9.2.3 was programmed in MATLAB model-files where the various constraints were formulated as objective components in the hard form. Applying the duality principle, the various maximization objectives were converted to minimization functions by simply negating them (Dantzig and Thapa, 1997 Deb, 2001). These model files were linked to the MOEA Toolbox to obtain the optimized values for the various control variables. LP was also applied and its solutions were used as a basis for comparison. 

---