Process equipment modeling using the moment method

Abstract

Process equipment models are needed in all stages of chemical process research and design. Typically, process equipment models consist of systems of partial differential equations for mass and energy balances and complicated closure models for mass transfer, chemical kinetics, and physical properties. The scope of this work is further development of the moment method for modeling applications that are based on the one-dimensional axial dispersion model. This versatile model can be used for most process equipment, such as chemical reactors, adsorbers and chromatographic columns, and distillation and absorption columns. The moment method is a numerical technique for partial differential equations from the class of weighted residual methods (WRM). In this work it is shown with examples how the moment method can be applied to process equipment modeling. The examples are: catalyst activity profiles in fixed-bed reactors, dynamic modeling of chemical reactors and fixed-bed adsorbers with axial dispersion, and steady-state and dynamic modeling and simulation of continuous contact separation processes with or without axial dispersion. An innovative field of application of the moment method is continuous-contact separation processes. The advantage of the moment method, compared to the state-of-the-art nonequilibrium stage model, is that the same level of numerical accuracy can be achieved with fewer variables. In addition, the degree of axial dispersion can be controlled precisely since only physical axial dispersion is introduced via the axial dispersion coefficient. When using axial dispersion models, special attention has to be paid to the boundary conditions. Using the moment transformation it is shown that the Danckwerts boundary conditions are appropriate for time-dependent models in closed-closed geometries. An advantage of the moment method, compared to other weighted residual methods such as orthogonal collocation on finite elements, is the ease with which boundary conditions are specified. The boundary conditions do not arise as additional algebraic equations. Instead, they simply appear as additive source terms in the moment transformed model equations. The second part of this thesis deals with the detailed closure models that are needed for process modeling. Relevance of some of the closure models is scrutinized in particular with two test cases. The first test case is gas-liquid mass transfer coefficients in trickle-bed reactors. It is shown that the correlation of Goto and Smith is appropriate for gas-liquid mass transfer coefficients in industrial trickle-bed reactors. The second test case is vapor-liquid equilibrium model parameters for binary systems of trans-2-butene and cis-2-butene and five alcohols. The Wilson model parameters for all binary systems are fitted against measurements with a total pressure apparatus. The measured pressure-composition profiles are compared against predictions by the UNIFAC and UNIFAC-Dortmund methods.