Although SuperCritical (SC) Fluid Extraction (SCFE) has been successfully applied commercially the last three decades, there is no systematic procedure or computational tool in the literature to scale-up and optimize it. This work proposes an algorithm to simulate dynamics in a multi-vessel (>= 3) high-pressure SCFE plant where extraction vessels operate in batches, and is thus forced to use simulated-countercurrent flow configuration to improve efficiency. The algorithm is applied to a three-vessel SCFE plant using a shrinking-core model to describe inner mass transfer in the substrate. As example, the extraction of oil from pre-pressed seeds using SC CO2 at 313 K and 30 MPa is simulated. After three cycles the process reaches a pseudo-steady-state condition that simplifies the estimation of plant productivity. Use of a three-instead of two-vessel SCFE plant increases oil concentration in the stream exiting the plant and decreases CO2 usage at the expense of increasing extraction time. (C) 2011 Published by Elsevier Ltd.