In distributed systems, transport phenomena coupled with chemical or metabolic reactions are functions of space. A computational method is outlined to acquire unknown system properties in distributed systems by problem inversion. Physical and chemical properties are estimated simultaneously. The finite-volume discretization method formulated in generalized curvilinear coordinates applied to inversion problem of arbitrarily complex geometries. Tire direct solution approach of the reacting transport problem through inexpensive acquisition of sensitivity information is presented. An inexact trust region method improves the convergence rate of the large-scale transport and kinetic inversion problem (TKIP). The case studies demonstrate a novel computational approach for quantifying unknown transport properties, as well as reaction or metabolic constants. Solutions to technological challenges is presented in computational fluid mechanics and biotransport using mathematical programming techniques for inversion of distributed systems. (c) 2006 American Institute of Chemical Engineers.