(140f) Modeling of Non-Newtonian Reactive Systems in Tubular Reactor

A vast majority of material processing in industry involves homogeneous phase reactions. These reactions are carried out in batch mode as well as continuous mode. The empty tubular reactors are widely used reactor systems for continuous processing. The heat effects due to these reactions necessitate the use of some heat removal/addition system with these reactors. Tubular reactors for Newtonian fluids have been studied extensively experimentally as well as through modeling. A vast majority of reactions involved in polymer processing, food processing, biochemical industries etc. are typical examples of non-Newtonian behaviour. The modeling studies dealing with non-Newtonian fluids are very limited. This study of non-Newtonian fluid reactions can lead to obvious benefits over experimental methodology. Most of the studies in non-Newtonian fluids are either based on convective models or on isothermal conditions. Novosad & Ulbrecht (1966) have modeled the reaction of power law fluids under laminar flow conditions, using residence time distribution concept to get conversions, neglecting the diffusional effects. Osborne (1975) studied convective model for non-Newtonian fluid tubular reactor under isothermal conditions. Tracer technique has been used for the systems with unknown rheological properties. For constant wall temperature conditions and adiabatic conditions, non-isothermal tubular polymerizers have been studied using finite volume method (Kleinstreuer & Agarwal, 1986). In actual systems, due to heat exchange, there is existence of temperature and concentration gradients and the effect further gets magnified due to rheological parameters. In this study, modeling of reactions of non-Newtonian fluids in tubular reactors with radial dispersion has been done. The reaction of non-Newtonian fluids has been modeled in non-isothermal non-adiabatic tubular reactor. Assuming a first order irreversible endothermic reaction of Ostwald-de-Waele power law fluids for the assumptions of constant wall temperature, the 2-D model is used to generate concentration and temperature profiles in axial and radial directions. The coupled mass balance, heat balance and velocity have been dealt with. The equations are converted to non-dimensional form. The model equations are solved by discretising using backward semi-implicit finite difference numerical technique. The discretised set of equations form a set of simultaneous equations which can be represented by matrix equation A.B = C. In this equation, the coefficient matrix A is tridiagonal banded matrix of MxM dimensions. This matrix equation is transformed such that the tridiagonal banded matrix is converted to an equivalent matrix of Mx3 dimension through Srivastava's technique (1983). This transformation economizes on computing space and time. The transformed set of coupled equations is solved by developing a program in FORTRAN, choosing an appropriate grid. The simulated results give the profiles for concentration and temperature in the reactor. In addition, the effect of various dimensionless parameters involved in the model, on these profiles is also investigated. An increase in a₁ and b₁ leads to an increase in conversion whereas temperature is not affected appreciably. On the other hand, an increase in a₂ leads to increase in conversion and temperature gain while an increase in b₂ gives a reduced conversion and temperature gain. The rheological parameter n also affects the reactor performance. An increase in rheological parameter leads to decrease in conversion and temperature. Also, the effect of n on velocity profile is also predicted. The distortion in velocity profile in moving along the reactor axis is higher for higher value of n.

References:

Kleinstreuer, C., & Agarwal, S. Coupled heat and mass transfer in laminar flow, tubular polymerizers. International Journal of Heat Mass Transfer, 29, 979-986, 1986

Novosad, Z., & Ulbrecht, J. Conversion in chemical reactions for isothermal laminar flow of non-Newtonian liquids in a tubular reactor of circular cross section. Chem. Engg. Sci., 21, 405-411, 1966

Osborne, F. T. Purely convective models for tubular reactors with non-Newtonian flow. Chem. Engg. Sci., 30, 159-166, 1975

Srivastava, V.K. The thermal cracking of benzene in a pipe reactor. Ph.D. Thesis, University of Wales, Swansea, U.K, 1983