Development And Validation Of Two-Dimensional Mathematical Model Of Boron Carbide Manufacturing Process
Boron carbide is produced in a heat resistance furnace using boric oxide and petroleum coke as the raw materials. In this process, a large current is passed through the graphite rod located at the center of the cylindrical furnace, which is surrounded by the coke and boron oxide mixture. Heat generated due to resistance heating is responsible for the reaction of boron oxide with coke which results in the formation of boron carbide. The whole process is highly energy intensive and inefficient in terms of the production of boron carbide. Only 15% charge gets converted into boron carbide. The aim of the present work is to develop a mathematical model for this batch process and validate the model with experiments and to optimize the operating parameters to increase the productivity. To mathematically model the process and understand the influence of various operating parameters on the productivity, existing simple one-dimensional (1-D) mathematical model in radial direction is modified first. Two-dimensional (2-D) model can represent the process better; therefore in second stage of the project a 2-D mathematical model is also developed. For both, 1-D and 2-D models, coupled heat and mass balance equations are solved using finite volume technique. Both the models have been tested for time step and grid size independency. The kinetics of the reaction is represented using nucleation growth mechanism. Conduction, convection and radiation terms are considered in the formulation of heat transfer equation. Fraction of boron carbide formed and temperature profiles in the radial direction are obtained computationally. Experiments were conducted on a previously developed experimental setup consisting of heat resistance furnace, a power supply unit and electrode cooling device. The heating furnace is made of stainless steel body with high temperature ceramic wool insulation. In order to validate the mathematical model, experiments are performed in various conditions. Temperatures are measured at various locations in the furnace and samples are collected from the various locations (both in radial and angular directions) in the furnace for chemical analysis. Also, many experimental data are used from the previous work to validate the computed results. For temperatures measurement, pyrometer, C, B and K type thermocouple were used. It is observed that results obtained from both the models (1-D and 2-D) are in reasonable agreement with the experimental results. Once the models are validated with the experiments, sensitivity analysis of various parameters such as power supply, initial percentage of B4C in the charge, composition of the charge, and various modes of power supply, on the process is performed. It is found that linear power supply mode, presence of B4C in the initial mixture and increase in power supply give better productivity (fraction reacted). In order to have more confidence in the developed models, the parameters of one the computed results in the sensitivity analysis parameters are chosen (in present case, linear power supply is chosen) to perform the experiment. Results obtained from the experiment performed under the same simulated conditions as computed results are found in excellent match with each other.