*Article* **Modeling of Spiral Wound Membranes for Gas Separations—Part II: Data Reconciliation for Online Monitoring**

**Diego Queiroz Faria de Menezes 1,\*, Marília Caroline Cavalcante de Sá 1, Tahyná Barbalho Fontoura 1, Thiago Koichi Anzai 2, Fabio Cesar Diehl 2, Pedro Henrique Thompson 2 and Jose Carlos Pinto 1**


Received: 24 July 2020; Accepted: 19 August 2020; Published: 25 August 2020

**Abstract:** The present work presents a methodology based on data reconciliation to monitor membrane separation processes reliably, online and in real time for the first time. The proposed methodology was implemented in accordance with the following steps: data acquisition; data pre-treatment; data characterization; data reconciliation; gross error detection; and critical evaluation of measured data with a soft sensor. The acquisition of data constituted the slowest stage of the monitoring process, as expected in real-time applications. The pre-treatment stage was fundamental to assure the robustness of the code and the initial characterization of collected data was carried out offline. The characterization of the data showed that steady-state modeling of the process would be appropriate, also allowing the implementation of faster numerical procedures for the data reconciliation step. The data reconciliation step performed well, quickly and consistently. Thus, data reconciliation allowed the estimation of unmeasured variables, playing the role of a soft sensor and allowing the future installation of a digital twin. Additionally, monitoring of measurement bias constituted a tool for measurement diagnosis. As shown in the manuscript, the proposed methodology can be successfully implemented online and in real time for monitoring of membrane separation processes, as shown through a real dashboard web application developed for monitoring of an actual industrial site.

**Keywords:** membrane; data reconciliation; real-time; online; monitoring
