The Nonideal Mixing Effect on the Selectivity Dynamic of Consecutive-Parallel Reactions in an Isothermal CSTR Based on Cholette’s Model

Jul 11, 2026

The nonideal mixing effect on selectivity dynamics for consecutive-parallel reactions in an isothermal continuous stirred tank reactor (CSTR) is analyzed using Cholette’s model. Mixing conditions are represented by μ = n/m, where n is the flow fraction and m is the dead-space fraction; μ = 1 denotes ideal mixing while μ≠1 denotes nonideal mixing. Phase-plane steady-state solutions are constructed for μ = 0.5, 1, and 2, revealing that larger μ increases final reactant and desired-product steady states. μ also reshapes transient selectivity extremes and startup trajectories, informing real reactor design and operation.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages11

Reading Time28 min

Introduction

Reaction schemes and selectivity background

Nonideal mixing and Cholette’s model context

Chane-Yuan Yang, Zhengwei Lin and Yu-Shu Chien* The nonideal mixing eﬀect on the selectivity dynamic of consecutive-parallel reactions in an isothermal continuous stirred tank reactor based on Cholette’s model [https://doi.org/10.1515/ijcre-2024-0023](https://doi.org/10.1515/ijcre-2024-0023)[ ](https://doi.org/10.1515/ijcre-2024-0023)Received January 29, 2024; accepted May 6, 2025; published online June 2, 2025 Abstract: This work presents the mixing conditions and kinetic reaction constant eﬀects on a continuous stirred tank reactor (CSTR) consecutive-parallel reactions selectivity dynamics in an isothermal CSTR based on Cholette’s model. The mixing condition eﬀect is accounted for using the parameter μ = n/m, where n is the ﬂow fraction to the reactor and m is the dead space fraction in the reactor. μ = 1 and μ≠1 represent, respectively, the ideal and nonideal mixing operations. The ﬁnal desired product yield steady state in the phase plane is ﬁrst constructed under reaction constant and mixing condition combinations, μ = 0.5, μ = 1 and μ = 2. The simulation results reveal that the larger the μ parameter, the higher the reactant ﬁnal steady state values, as, and the desired product, bs. For μ = 0.5 < 1, the short circuit ﬂow or channeling eﬀects were less than that of the dead volume in a real CSTR, leading to lower both ﬁnal steady state values, as and bs, than those under ideal mixing, μ = 1. On the other hand, under the nonideal mixing conditionμ =2>1, i.e., the short circuitﬂoweﬀector channeling larger than the dead volume in thereactor, resulted ina higher ﬁnal steady state (as,bs) than those under ideal mixing. A comparative analysis of the mixing condition eﬀects reveals that a higher μ value reduces the transient maximum selectivity regions while increasing the transient minimum selectivity regions. In the selectivity dynamic simulations, the phase plane is divided into a transient extreme yield region and monotonic yield variation region. It is observed, for the ﬁrst time, that a higher μ value diminishes the transient maximum selectivity region area while expanding the transient minimum selectivity region area in the phase plane. Additionally, the trajectory from the start up to the ﬁnal steady state is *Corresponding author: Yu-Shu Chien, Chemical and Materials Engineering, National Chin-Yi University of Technology, Taichung, Taiwan, E-mail: [yschien@ncut.edu.tw](yschien@ncut.edu.tw) Chane-Yuan Yang and Zhengwei Lin, Chemical and Materials Engineering, National Chin-Yi University of Technology, Taichung, Taiwan. [https://orcid.org/0000-0002-6212-563X](https://orcid.org/0000-0002-6212-563X) (C.-Y. Yang) altered due to nonideal mixing. These novel ﬁndings, which have not been previously published, hold direct relevance for the design and operation of real reactors. Given that ideal mixing is rarely achievable in practical CSTRs, our results oﬀer valuable insights for optimizing reactor design and start-up policies to enhance the desired product transient yield. Keywords: consecutive-parallel reaction; selectivity dynamics; nonideal mixing; CSTR; Cholette’s model 1 Introduction Chemical reactions exhibiting selective behavior, often referred to as complex reactions, present signiﬁcant challenges in reactor design due to their practical importance. This study focuses on maximizing the desired product yield under speciﬁc conditions. For understanding these dynamics by employing analytic transient solutions to address the selectivity behavior in consecutive-parallel reactions within a continuous stirred tank reactor (CSTR), Varma and DeVera [1] provided a foundation expressed as. ⎧ k1 k k2 k ⎨ A → 1 B → 2 C (1) ⎩ A k3 D and Van de Vusse reaction as ⎧ k1 k k2 k ⎨ A → 1 B → 2 C (2) ⎩ 2A k3 D where A is the reactant species, B and C are the desired and undesired product species, respectively. Due to the computational limitations, lots ofeﬀorts were devoted to analytical solutions for the

FAQs

How is nonideal mixing quantified in this study?

Nonideal mixing is captured by the parameter μ = n/m, where n is the flow fraction entering the reactor and m is the dead-space fraction. μ = 1 corresponds to ideal mixing, while μ≠1 represents nonideal mixing.

What trend does μ show for final steady-state values of reactants and the desired product?

Simulation results show that increasing μ leads to higher final steady-state values for the reactant (as) and the desired product (bs).

How does nonideal mixing affect transient selectivity maxima and minima?

A comparative analysis indicates that higher μ reduces the transient maximum selectivity region while expanding the transient minimum selectivity region within the phase plane.

Why are these results relevant for real CSTR design and startup?

Because ideal mixing is rarely achievable in practical CSTRs, the findings provide guidance for optimizing reactor design and startup policies to enhance desired-product transient yield.

Jul 11, 2026

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