OPTIMUM CONCENTRATION PROFILES OF SULFURIC-ACID IN SULFONATION PROCESS OF AROMATIC-HYDROCARBONS .2. SULFONATION PROCESS

The work is an extension of previous study on the determination of the optimum temperature profile for the heterogeneous catalytic reactions [3-6] and it is concerned with the optimum concentration profiles of the reactant for the maximizing yield of one of the products in parallel or consecutive reactions in liquid system. The sulfonation process of aromatic hydrocarbons (toluene, ethylbenzene, isopropylbenzene etc.) is used as an example. The sulfonation process is usually carried out in a batch reactor. Three cases are possible: (a) the process is carried out homogeneously; (b) the aqueous phase is a continuous phase, the organic phase being the dispersed phase; (c) the organic phase is a continuous phase, the aqueous phase being the dispersed phase. In the first case we have to do only with one phase and as far as the case (b) and (c) are concerned, two liquid phase can appear. The balance equations can be written down as: - for the sulfonation process modeled as a system of three parallel reactions: Eqs. (2) and (3) or (4) and (5) or (6); - for the sulfonation process modeled as a system of two consecutive reactions: Eqs. (7) and (8) or (9). In order to derive the balance equations the following assumptions were used: (1) concept of enhancement factor (in the case (b)) of effectiveness factor (in the case (c)) is applicable [2]; (2) reaction rate constants can be expressed by Eq. (1) [1]; (3) all drops are spherical in shape and of equal size; (4) the number of drops is very large and it can be treated as a continuous variable (in the case (b)); (5) the radius of drops remained constant in a bath process; (6) there is no liquid circulation in a drop (in the case (c)); (7) the system is isothermal. The optimization problem is formulated in the form of Eqs. (10) or (11). Using the Pontriagin's maximum principle several conclusions concerning the shape of optimal concentration profiles of sulfuric acid have been drawn. Some of them are presented below: (1) For the sulfonation process modeled as a system of three parallel reactions the optimal concentration profiles are non-falling curves, which end but not necessarily by maximum feasible concentration of sulfuric acid. (2) If the sulfonation process is modeled as a system of two consecutive reactions, the optimal concentration profiles of sulfuric acid are non-rising curves. The optimal concentration profiles need not to start with constant acid concentration c(Smax). It is worthy to note that these conclusions were obtained without performing any numerical computations.