Optimization of ammonia reactor using shooting methods

The work in this paper concentrates on shooting methods application in the optimal design problem of an ammonia synthesis reactor. This paper presents an alternative approach in solving the boundary value problem. In this study, the optimal design problem aims at obtaining the optimal reactor length with maximum economic returns corresponding to a temperature of feed gas at the top of the reactor (top temperature) of 694K. The main objective of this paper is to investigate whether the ammonia design problem can be solved using shooting methods coupled with existing standard optimization algorithm without having to resort to specialized numerical techniques as presented in earlier literature. Shooting methods, namely single and multiple-shooting methods are used. The resulting nonlinear optimization problem is solved using the ordinary differential equation (ODE) integration routine 'ode45' and the optimization routine 'FMINCON' available in MATLAB. From the results obtained, the solution yields an economic return of $5.015 × 106 per year at an optimum reactor length of 6.695m, which agree considerably well with the latest literature work using the relatively complicated Differential Evolution (DE) method. This result signifies the potential credibility and the sheer simplicity of shooting methods in solving the problem, where fairly accurate results can be obtained just by using standard numerical optimization algorithm.