Three lump model

All the works just cited have an important and common assumption the well-known, three-lump Weekman model with three kinetic constants. This three-lump model was a significant achievement, but it lumps together gas and coke, which are clearly different. Therefore, we consider it absolutely necessary to expand this model by using a five-lump model with eight cracking constants and the following definitions A = feedstock (bp > 350 °C), O = gas oil (bp 221-350 °C), E = gasoline (bp 36-221 °C), G = gas (bp < 36 ° C), and C = coke (by combustion). 

Figure 1. Yield and conversion versus initial coke content The points show the experimental values, the curves are computed value with a three lump model, l conversion, gasoline, o gas, a coke yields. The experimental conditions S and 1 are given in table 1.

Figure 12.3. Mobil Oil s three-lump model for gas oil cracking.

A general model that considers nonequilibrium oxygen tension conditions between the erythrocytes and plasma has been derived. The rate of oxygen transport between the erythrocyte and plasma is assumed to be a function of the difference between the equilibrium and dynamic oxygen dissociation curves, and the rate of oxygen transfer to the tissue is based on the oxygen tension difference between the plasma and tissue. The three-lump model can be written as follows,... 

By assuming that equilibrium exists between the erythrocytes and plasma, the three-lump model is reduced to two lumps. The system equations for the tissue lump-capillary lump model are developed by writing oxygen material balances for the tissue and capillary separately or by summing the erythrocyte and plasma equations for the three-lump model. The two-lump model (21) has been used in this investigation and can be represented by the following set of equations (Figure 1). 

According to the three lump model, the rates of gas oil cracking and gasoline cracking may be written as ... 

The deposition of coke on the catalyst results in rapid activity decay and hence a catalyst decay function is multiplied by the intrinsic rate to give the actual rate. It is normally assumed that the same active sites will crack both gas oil and gasoline molecules, therefore the activity decay functions and 2 are assumed equal (Weekman, 1968). In general, the catalyst activity is dependent on the carbon laid down and is thus related to the time the catalyst is exposed to hydrocarbons. Then, to completely describe the kinetics of cracking according to the three lump model involves the determination of the parameters k, ki, kj and the deactivation function. ... 

The three lump model has been successful in adequately describing gasoline selectivity behaviour from laboratory experimental data from studies done for one specific feedstock with one particular catalyst (Pachovsky and Wojciechowski, 1971, 1975a, 1975b 1975c John and Wojciechowski, 1975 Campbell and Wojciechowski, 1969, 1971 Gross et al., 1974 Corella et ai., 1985). As well, the model as been used in commercial and pilot transfer line units with reasonable success (Shah et al., 1977 Paraskos et al., 1976 Corella et al., 1986). 

The ten-lump model has shown success in adequately describing selectivity and conversion behaviour in pilot plant and commercial risers for a wide variety of feeds without modification of the rate constants. However, the simplicity of kinetic representations such as the ones for the three-lump model are partially lost. In using higher lumping models where the number of parameters is significantly increased means that greater amounts of experimental data are also required. 

Two commercial feedstocks A and B, whose characteristics are reported in Table 1, were cracked with both Octacat and GX-30 catalysts for different reaction times (3, 5, 7 and 10 seconds) and temperatures (500, 525 and 550 C) are shown in Figures 9 to 12. In these figures the symbols refer to experimental results while the lines show model predictions (using the three lump model with exponential decay). The trends in experimental conversion show that with increasing reaction time conversion increases which is an expected result due to the nature of the... 

To describe the kinetics of catalytic cracking the three lump model was used in combination with three different catalyst deactivation model. Overall gas oil cracking kinetic constants (k or k ) along with the decay parameters for the three decay models were determined for four feedstock-catalyst combinations. An example of these evaluations is presented in Table 4. 

These constants were obtained by solving the gas oil mass balance equation for the three lump model (see equation 3.5). For the case where the power law decay equation was used, the overall gas oil cracking constant was called k, since it has different units than k (equation 3.10). 

The overall cracking constants for the pure hydrocarbon groups (P, Nj, and A,) are presented in Table 5. Values obtained using both the exponential decay function and the power law function are presented. These constants were obtained by solving the light lump equation (equation 3.13) in the 8-lump model with Yj set to zero. This is equivalent to using the three lump model for each separate light lump oil mixture with first order kinetics. 

Symbol for gas oil in the three lump model, aromatic compounds in the 8-lump model Symbol for gasoline lump in the three lump model Symbol for light gases plus coke lump Concentration of gas oil (gmol/cm )... 

The HCR reaction was represented by a three-lump model as follows (Bhaskar et al., 2004) ... 

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