Synthesis of Reaction Pathways via Systematic Integration

The environmental pollution has become, during the recent years, a crucial problem of public concern, and the authorities are requested to realize “pollution prevention” with systematic methods to replace the conventional “end-of-pipe” treatment techniques. The specification of the most desirable reaction routes that connect the initial reactants and the desired products, or known as reaction path synthesis, represents a key step in arriving at environmentally benign process designs. One of the most famous examples is the Solvay Soda Ash Process, which converts sodium chloride (salt) and calcium carbonate (limestone) into sodium carbonate (soda ash) and calcium chloride by six reaction clusters that are equivalent to the infeasible overall target reaction from a mass balance point of view, while are all thermodynamically feasible under industrial conditions. In this work, we will present the synthesis of thermodynamically feasible reaction pathways to achieve a thermodynamically infeasible overall target reaction, from a mathematical prospective. A notion of irreducible reaction (IRR) whose reactive system has one and only one degree of freedom, was initially introduced, and the particular properties of IRRs were elaborated. An efficient algorithm which is based on Singular Value Decomposition (SVD) to enumerate the finite number of IRRs from a large species database, with an arbitrarily pre-specified maximum number of substances allowed in each individual reaction, was developed and its completeness was strictly proved using linear algebra theories. Involved with only operations on matrices, this algorithm circumvents the conventional Mixed-Integer Linear Programming (MILP) methods and thus, the computational load can be significantly reduced, especially in high dimensional cases. Following the introduction of IRRs, the issue of synthesis of thermodynamically feasible reaction pathways to realize a thermodynamically infeasible overall reaction was formulated and solved as an optimization problem to satisfy overall mass balance, thermodynamics and other chosen performance criteria and constraints.