Modeling and identification of pH processes

This paper presents in a complete and detailed manner the modeling of pH processes. The model is strictly based on the physical balance equations of mass and charge. The model exactly represents the balance equation, it is proven that polyprotic substances can be represented uniquely by a combination of monoprotic substances equivalent to the real acids, bases and salts that compose the solution. A general differential algebraic equation model is derived for the CSTR arrangement. Observability conditions for the solution inside the CSTR are derived using a reduced model and based on these observability conditions a minimal description for the chemical solution is derived. The balance equation is shown to be monotone, hence the solution of this equation is unique and well defined for each value of pH. This establishes the validity of nonlinear feedback linearization techniques which require the inverse of the static nonlinearity. Two identification methods are proposed: the nonnegative least squares algorithm to find the influent concentrations when the dissociation constants pK´s are known or to find a set of fictitious concentrations that best represent an unknown model using a fixed and ample set of fictitious pK´s. The nonlinear optimization algorithm operating in cascade with the nonnegative least squares algorithm determines the set of pK´s and respective concentrations that best approximate the influent composition.