Mixed Integer Nonlinear Programming model for the optimal design of fired heaters

In this paper, a mathematical optimization model for the optimal design of industrial furnaces/fired heaters is presented. Precisely, a detailed Mixed Integer Nonlinear Programming (MINLP) model including operational and geometric constraints is developed to get an efficient furnace design. Discrete decisions connected with the geometric design such as number of tubes in convection and radiation sections, number of shield tubes, number of passes and number of tubes per pass are modelled by using integer variables. Continuous variables are used for process conditions (temperatures, flow-rates, pressure, velocities, pressure drops among others). The mathematical model and the solution procedure are implemented in General Algebraic Modelling System (GAMS), Brooke [A. Brooke, D. Kendrick, A. Meeraus, A. A. GAMS – A User’s Guide (Release 2.25), The Scientific Press, San Francisco, CA, 1992]. Based on a typical furnace configuration, several applications are successfully solved by applying the proposed MINLP model. In this paper, three case studies with increasing complexity are presented. In the first case study, the accuracy of results from the proposed model is compared satisfactorily with literature. In the second case study, the MINLP model is applied to optimize the fire heater’s efficiency. Finally, the total annual cost of the fired heater is minimized in the Case Study III. Also, a sensitive analysis of the unitary cost of fuel and capital investment is investigated. The developed model is characterized by its robustness and flexibility.