Approximate process dynamics of certain nonlinear systems can be estimated by elementary quadratures using a modal approach. The transient response including quadratic nonlinearities is determined by the eigenvalues, eigenvectors, and adjoint eigenvectors of the linearized system equations. The only restriction is that the dominant eigenvalue of the linearized system must be widely separated from the next slowest mode. Several process models satisfy this requirement.
The method is illustrated by application to a fourth-order model of a fluidized bed. The dynamical response is in agreement with numerical solutions to the complete model equations, including estimates of finite regions of stability.