Coupled heat/mass transfer differential reactor

The steady-state model consists of a set of coupled ordinary differential and algebraic equations. The simulation is obtained by integrating simultaneously the mass-balance equations for the gas and liquid phases in the axial direction of the reactor using a fourth-order Runge-Kutta method. The heat balance is used only for the simulation of the industrial reactors. The solid phase algebraic equations are solved between integration steps with the Newton-Raphson method. Physical properties and mass-transfer coefficients are also updated in every integration step. 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

This problem requires an analysis of coupled thermal energy and mass transport in a differential tubular reactor. In other words, the mass and energy balances should be expressed as coupled ordinary differential equations (ODEs). Since 3 mol of reactants produces 1 mol of product, the total number of moles is not conserved. Hence, this problem corresponds to a variable-volume gas-phase flow reactor and it is important to use reactor volume as the independent variable. Don t introduce average residence time because the gas-phase volumetric flow rate is not constant. If heat transfer across the wall of the reactor is neglected in the thermal energy balance for adiabatic operation, it... 

This variety of reactor types reflects the complex interaction between chemical reaction and mass and heat transfer. In spite of this complexity, in principle every reactor can be described by the fundamental balance equations for the preservation of mass, energy, and impetus. These form a system of five partial differential equations (PDFs), coupled through temperature, concentation, and three rate vectors [Damkohler 1936, Platzer 1996, Adler 2000]. 

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