Solute transport with multisegment, equilibrium-controlled, classical reactions: Problem solvability and feed forward method's applicability for complex segments of at most binary participants

The feed forward (FF) method derives efficient operational equations for simulating transport of reacting solutes. It has been shown to be applicable in the presence of networks with any number of homogeneous and/or heterogeneous, classical reaction segments that consist of three, at most binary participants. Using a sequential (network type after network type) exploration approach and, independently, theoretical explanations, it is demonstrated for networks with classical reaction segments containing more than three, at most binary participants that if any one of such networks leads to a solvable transport problem then the FF method is applicable. Ways of helping to avoid networks that produce problem insolvability are developed and demonstrated. A previously suggested algebraic, matrix rank procedure has been adapted and augmented to serve as the main, easy-to-apply solvability test for already postulated networks. Four network conditions that often generate insolvability have been identified and studied. Their early detection during network formulation may help to avoid postulation of insolvable networks.