Modeling Chemical Reactions Using Bond Graphs Dr. Jürgen Greifeneder ABB Corporate Research Center Wallstadter Str. 59 68526 Ladenburg, Germany greifeneder@eit.uni-kl.de Prof. Dr. François E. Cellier, SCS Fellow Computer Science Department ETH Zürich CH-8092 Zürich, Switzerland FCellier@Inf.ETHZ.CH Keywords: Chemical reactions, Modelica, Bond graphs Abstract This article offers a general methodology for modeling basic chemical reactions and carries forward a series of papers on modeling thermodynamic behavior using true rather than pseudo-bond graphs. In order to make processes of heating and expansion within the mixture visible, our approach does not deal with one overall vo- lume and the overall entropy –as would be normal for classical chemistry– but rather with separated entities, one for each compound. Furthermore, assumptions of quasi- stationary or equilibrium conditions are minimized to en- sure the largest possible degree of generality in the con- clusions reached. It will be shown, that chemical reactions can be mod- eled as transformative behavior, which makes their exter- nal behavior linear and therefore allows for superposing several chemical reactions. While the mass flows (respectively molar flows) are assumed to be determined directly from Arrhenius’ equa- tion and the underlying stoichiometry, the determination of entropy and volume flow processes needed a more ex- tensive discussion. A bondgrapher’s Modelica model of the HBr-synthesis based on the assumption of ideal gas serves as an example of the presented theory of chemical reaction dynamics. 1 INTRODUCTION Dealing with macroscopic mass flows, the mass that flows through the system has to be modeled explicitly, as it carries with it its stored internal free energy, which is thus transported from one location to another in a non- dissipative fashion. In the most general sense, thermody- namics ought to be described by distributed parameter models. Since bond graphs are geared to be used for the description of lumped parameter models only, a simplify- ing assumption will be made, in that the system to be modeled is compartmentalized, whereby each compart- ment is considered to be homogeneous. New bond-graphic macro-elements were introduced in the previous papers [1][2][3][4] to describe the energy storage within a compartment as well as the mass (and energy) flows between neighboring compartments. The first of them [1] discussed the modeling of conductive as well as convective flows of a single homogeneous sub- stance through a homogeneous medium. The second one [2] discussed the phenomena associated with phase change, i.e., it discussed –from a bondgrapher’s perspec- tive– phenomena such as evaporation and condensation, solidification, melting, and sublimation. The third paper in the series [3] dealt with the difficult problem of modeling multi-element systems. Therefore the assumption of ho- mogeneous, ideally mixed compartments was needed. ‘Ideally mixed’ here means that the molecules are distri- buted at random, i.e., a prediction of what molecule be- comes a neighbor of which other molecules is not possi- ble. These conceptual systems have been modeled by in- troducing one energy storage element for each component of the mixture and by connecting them using pressure- volume-exchange and heat-exchange elements. The latest of the previous papers [4] introduced the corresponding thermal-bond-library for Dymola [5]. 2 BONDS, MULTI-BONDS, AND THERMO-BONDS In this section, a short summary of the three types of bonds that populate our three bond graph libraries, Bond- Lib [8], MultiBondLib [9], and ThermoBondLib [4], is provided. The basic bonds are our regular (black) bonds as shown in Fig. 1. Fig. 1: Regular bonds. Regular bonds carry two variables, the effort, e, and the flow, f. Their connectors, the gray dots to the left and the right of the bond carry a third variable, the directional variable, d. The directional variable is set by the bonds. It assumes a value of +1 at the side of the harpoon, and a value of -1 at the opposite end of the bond. The direction- al variable is used by the junction models to sum either the flows or the efforts up correctly. 110