(181f) Rcc Algorithm for Automated Attainable Regions Analysis: Methanol Synthesis

For reactor network synthesis, attainable regions analysis provides a set of all possible product states that can be realized from given chemical reaction scheme with underlying kinetics and specified feed, permitted fundamental processes and system constraints ^[1]. This set of all possible system output states that can be achieved by application of all permitted fundamental processes and or combinations thereof is termed the attainable region (AR). The boundary of the attainable region sets the limit to all achievable states and it is therefore of special interest as it is in most cases, where a given objective can be optimised. Even though the general theory of AR analysis has been developed over the years ^[2,3], there is no known sufficiency conditions that characterise the boundary of the AR. Necessary conditions have been derived, which a nominated boundary has to satisfy in order to be considered a candidate AR. It is this absence of the sufficiency conditions that make identification of AR boundaries an intricate procedure guaranteeing no certainty of the complete or true result.

Feinberg demonstrated by use of mathematical proofs arising from the theory of geometric optimal control that the AR boundary, for systems considering fundamental processes of isothermal reaction and bulk mixing, is outlined by special types of reactors ^[4,5]. These special reactors that are characterized by stringent mathematical conditions give access to extreme points from which reaction manifolds (representing plug flow reactors) and mixing planes that form the final shape of the AR boundary originate. For reaction and mixing, these special types of reactors are always reactor structures in which simultaneous reaction and mixing occur optimally under governance of some control policy ^[4,5]. Feinberg derived the mathematical equations that the control policies have to obey in order for a special type of reactor structure to occur on the AR boundary. From these proofs it can be asserted that a candidate AR can be identified primarily by determining the structures that outline the boundary giving access to extreme points from which fundamental process manifolds emanate. This work proposes an automated technique for identifying candidate attainable regions using recursive constant control policy algorithm (RCC). This approach uses iterative application of constant control policies to approximate the optimal state varying optimal control policy that govern the occurrence of a special reactor type on the boundary.

For a system considering fundamental processes of reaction and mixing, the special types of reactors that delineate the outline structure of the AR boundary are the critical continuous flow stirred tank reactor (CFSTR) and the critical differential side stream reactor ^[4,5]. Mathematically, it can be shown that the CFSTR is a special type of a DSR where the vector representing the combined rate of reaction and bulk mixing diminishes to zero. In this work we propose that the critical CFSTR therefore occur on the AR boundary at discrete points where the vector field of the critical DSR goes through a node. By identifying critical DSR's, the critical CFSTR's will be automatically identified at the DSR nodes. The support of this proposition has been demonstrated with results from case studies. Once the critical DSR's and CFSTR's have been identified, the boundary of the attainable regions can be completed by application of plug flow reactor (PFR) and mixing planes that emanate from critical structures. We have demonstrated the practicality and applicability of the automated RCC technique to identify candidate ARs. The RCC algorithm has been used to solve various case studies ranging from the simple van de Vusse mass action kinetic reaction scheme in three dimensional and computer intensive four dimensional system to several industrial case studies that extend the applicability of the technique to non-isothermal reaction schemes considering fundamental processes of reaction, bulk mixing, and heat transfer such as the generic first order exothermic reversible reaction, ammonia synthesis, methanol synthesis and oxidative dehydrogenation of 1-butene.

Attainable regions analysis is used to identify optimal reactor networks configurations for the examples detailed below that have previously been thought to be impossible. This procedure is carried out in an easy automated manner using the RCC technique. The method is implemented into an easy to use software routine using MATLAB^®. Due to the robustness of the underlying RCC algorithm, the software package can be compiled into a custom package that allows the end user to enter reaction scheme, select system variables and permitted fundamental processes as well as control policies. Due to the built-in data tracking capabilities of the RCC method, interpretation of the resulting attainable regions boundary into optimal reactor network structure can also be done automatically.

This paper illustrates how the RCC method can be used to identify optimal reactor structures for methanol synthesis via attainable regions analysis. In the methanol synthesis system, the water gas shift reaction can be carried out separately or can be done along with methanol formation reaction using a WGS active catalyst. By using the RCC algorithm we are able to show the best configuration relative to an economic evaluation. Different reactor structures are considered to incorporate fundamental processes of reaction, bulk mixing, heating and cooling. The results obtained are compared for consistency with the reactor sequencing in current methanol synthesis industrial practice.