Formal Verification of Isothermal Chemical Reactors

Abstract

Chemical reactors are dynamic systems that can be described by systems of ordinary differential equations (ODEs). Reactor safety, regulatory compliance, and economics depend on whether certain states are reachable by the reactor, and are generally assessed using numerical simulation. In this work, we show how differential dynamic logic (dL), as implemented in the automated theorem prover KeYmaera X, can be used to symbolically determine reachability in isothermal chemical reactors, providing mathematical guarantees that certain conditions are satisfied (for example, that an outlet concentration never exceeds a regulatory threshold). First, we apply dL to systems whose dynamics can be solved in closed form, such as first-order reactions in batch reactors, proving that such reactors cannot exceed specified concentration limits. We extend this method to reaction models as complex as Michaelis-Menten kinetics, whose dynamics require approximations or numerical solutions. In all cases, proofs are facilitated by identification of invariants; we find that conservation of mass is both a principle proved from the ODEs describing mass action kinetics as well as a useful relationship for proving other properties. Useful invariants for continuous stirred tank reactors (CSTRs) were not found, which limited the complexity of reaction networks that could be proved with dL. While dL provides an interesting symbolic logic approach for reachability in chemical reactions, the bounds we obtained are quite broad relative to those typically achieved via numerical reachability analyses.