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

The aim of this work is to solve an identification problem in plug-flow chemical reactors. This leads to an optimization problem involving parameters and for which the adjoint method is introduced for calculating the gradient of the objective function. An adjoint-based algorithm for parameter identification problems in systems of partial differential equations is presented. The algorithm calculates the gradient of the objective function with respect to the unknown parameters by using an adjoint method, significantly reducing the computer time. We apply this methodology to the problem of estimating a set of unknown parameters appearing in chemical reaction models when a plug-flow reactor is used. This is done by solving 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 obtained with it are shown. The efficiency of the adjoint method, compared with the classical formula of incremental quotients, is also presented.