Optimal heating profiles in tubular reactors with solid-phase axial wall conduction for isothermal operation

Optimal heat input profiles to maintain near isothermal operation in endothermic tubular reactors with axial solid-phase conduction were derived using a one-dimensional steady state plug flow model capturing the main transport phenomena in flow reactors. A cost criterion to minimize the deviation from isothermality was defined and optimal control theory is applied to calculate the optimal heating profiles as a function of position. It is shown the perfect isothermality is mathematically possible only if the wall conduction term is infinitesimally small. Using singular optimal control theory, analytical expressions of the input profiles are derived including a simple criterion for near-isothermal operation in terms of dimensionless reactor parameters.