Contents lists available at ScienceDirect Thermochimica Acta journal homepage: www.elsevier.com/locate/tca An extension of the NPK method to include the pressure dependency of solid state reactions Markus Deutsch a , Felix Birkelbach b, ⁎ , Christian Knoll c , Michael Harasek a , Andreas Werner b , Franz Winter a a TU Wien, Institute of Chemical Engineering, 1060 Vienna, Austria b TU Wien, Institute for Energy Systems and Thermodynamics, 1060 Vienna, Austria c TU Wien, Institute of Applied Synthetic Chemistry, 1060 Vienna, Austria ARTICLE INFO Keywords: Heterogeneous kinetics Pressure dependency NPK CdCO 3 ABSTRACT An novel method to identify the pressure dependency for reactions of the type A(s) ⇌ B(s) + C(g) is proposed. It is an extension of the non-parametric kinetic analysis (NPK) method as it identifies the pressure dependency in addition to the temperature and conversion dependency of the reaction. This is done by analyzing kinetic data in a three-dimensional data space (conversion, temperature, pressure) and attributing the variation of the con- version rate to these independent variables. Thus a reduction from a three-dimensional problem to three one- dimensional problems is achieved. The derivation of a kinetic model can then be performed for each dependency independently, which is easier than deriving a model directly from the data. This work presents the basic ap- proach of the identification and combination of the three dependencies to build a full kinetic model. Also, the interpretation of the model to achieve a physically motivated model is illustrated. Then the method is applied to identify the complex reaction kinetics of the decomposition of CdCO 3 based on a set of thermogravimetric measurements. It is shown that it is possible to identify interaction terms between the dependency terms. 1. Introduction The kinetics of a reaction often determines its technological ap- plicability and directly influences how economically feasibly a process based on that reaction is. Knowledge of the reaction kinetics is funda- mental to choose optimal reaction conditions and to achieve satisfying conversion. Many solid-state decompositions follow the simple reaction ⇌ + A(s) B(s) C(g) (1) The kinetics of such reactions is often modelled based on the reac- tion rate dα/dt. It is generally described as a product of the contribu- tions of three independent variables, the conversion α, the temperature T and the pressure p by the differential equation = α t fαkThp d d () ( ) ( ) (2) In case of reactions that follow Eq.(1) the pressure relevant is the partial pressure of the gaseous component C. The literature on solid state kinetic identification focuses mainly on the determination of conversion dependency f(α) and temperature dependency k(T), while the identification of the pressure dependency h(p) is often neglected [1]. Yet the pressure dependency is of great interest for reactor design since some reactor types, e.g., fluidized bed reactors, feature high concentration gradients of the reactant gas across the bed height. To take this effect into account, knowledge about the pressure dependency of the reaction is absolutely necessary [2]. To describe the conversion dependency f(α) different conversion models are used. These conversion models are mathematical descrip- tions of the measured process during the reactions. For solid state re- actions, various different models have been proposed. Some of them represent physical processes (e.g. nucleation, diffusion) as their math- ematical description has been derived on certain mechanistic assump- tions. Others are purely mathematical. Khawam et al. and Dickinson et al. describe 28 different models and give an overview over the dif- ferent models and their underlying assumptions [3,4]. Table 1 shows the models, relevant for this work. The temperature dependency is usually described by the Arrhenius equation = − kT A E ( ) exp RT a (3) http://dx.doi.org/10.1016/j.tca.2017.05.019 Received 17 March 2017; Received in revised form 3 May 2017; Accepted 25 May 2017 ⁎ Corresponding author. E-mail address: felix.birkelbach@tuwien.ac.at (F. Birkelbach). Thermochimica Acta 654 (2017) 168–178 Available online 30 May 2017 0040-6031/ © 2017 Elsevier B.V. All rights reserved. MARK