Determining the optimization scope is a major issue whenever implementing Real-time Optimization (RTO). Ideally, the optimization problem should encompass the whole plant and not a single unit, which represents only a local subset of the problem. However, if the standard RTO method, the two-step approach (TS), is applied to the entire plant, the whole system needs to be at steady-state (SS) in order to initiate the optimization cycle. This condition is rarely found in practice. One alternative is to apply Real-time Optimization with Persistent Parameter Adaptation (ROPA). ROPA is an RTO variant that integrates online estimators to the standard TS framework and avoids the need of waiting for steady-state to trigger the optimization cycle. However, the problem shifts to obtaining a dynamic model of the entire plant, which can be challenging and time consuming. This paper proposes a variant of ROPA, named asynchronous ROPA (asROPA), where the plant-wide model is partitioned into submodels and, depending on their characteristics, their parameters are updated using either online or steady-state estimators. Consequently, it is not necessary to obtain a dynamic model for the whole process. This asynchronous updating strategy allows the plant-wide model to be up-to-date to the process and the plant-wide optimization can be scheduled at any arbitrary time. The new strategy is applied to a case study consisting of a system whose model can be partitioned into a separation and a reaction submodel. The plant-wide results indicate that asROPA reacts much faster to the disturbances in comparison to the TS approach, improving the overall economic performance and is able to drive the system to the plant-wide optimum. Additionally, a strategy for partitioning the process and choosing the estimation strategy for each partition is proposed. (C) 2020 Elsevier Ltd. All rights reserved.