Identification problem in plug-flow chemical reactors using the adjoint method

The aim of this work is to solve identification problems in plug-flow chemical reactors. For this purpose an adjoint-based algorithm for parameter identification problems in systems of partial differential equations is presented. The adjoint method allows us to calculate the gradient of the objective function and the constraint functions with respect to the unknown parameters significantly reducing the computer time. This leads to solve a minimization problem, in which an objective function is defined in order to quantify the mismatch between the observed data and the numerical solution of the parameterized chemical model. For solving the initial and boundary-value problem we use finite-difference schemes. More precisely, we propose a second-order BDF method initialized with a first-order one. The algorithm proposed was implemented in a computer program and some numerical results are shown. The efficiency of the adjoint method, compared with the classical formula of incremental quotients, is also presented.