Resolving systems of ordinary differential equations in a naphtha reforming process: Comparison of laplace transform and numerical methods

Abstract

Developing a simple technique to generate important hydrocarbon products as raw feed materials would benefit the petrochemical industry. This paper presents the Laplace transform method in comparison with the numerical method of resolving systems of ordinary differential equations in a reforming process in a tubular reactor for the production of essential hydrocarbon components as petrochemical feedstocks. The feed species, lumped naphtha (paraffin), was fed into the tubular reactor for reforming (cracking) into essential hydrocarbon components including naphthenes, aromatics, and gases (methane, ethane, propane, and butane). Material and energy balance principles were applied to obtain nonlinear reactor models as a function of mole fractions and temperature. Laplace transform was then used to resolve the nonlinear reactor models into algebraic forms to describe the transformations in the depleting species and the formation of the target products in the reactor. Real plant (industrial) data were further used to simulate the models while literature data were used for model comparison. The comparison of the models was based on numerical and analytical results obtained for the mole fractions and temperature. With the analytical method as a reference, results showed that the numerically simulated results deviated from the analytical results by 0.10, 1.93, 16.09, 22.34, and 4.511% for paraffin, naphthene, aromatics, gases, and temperature, respectively; all within the recommended values for reactor cracking operations. This suggests that the analytical approach yielded better results than the numerical method.