A set of constitutive relationships accounting for residual NAPL in the unsaturated zone

Although laboratory experiments show that non-aqueous phase liquid (NAPL) i s retained in the unsaturated zone, no existing multiphase flow model has b een developed to account for residual NAPL after NAPL drainage in the unsat urated zone. We developed a static constitutive set of saturation-capillary pressure relationships for water, NAPL and air that accounts for both this residual NAPL and entrapped NAPL. The set of constitutive relationships is formulated similarly to the set of scaled relationships that is frequently applied in continuum models. The new set consists of three fluid-phase sys tems: a three-phase system and a two-phase system, that both comply with th e original constitutive model, and a newly introduced residual NAPL system. The new system can be added relatively easily to the original two- and thr ee-phase systems. Entrapment is included in the model. The constitutive rel ationships of the non-drainable residual NAPL system are based on qualitati ve fluid behavior derived from a pore scale model. The pore scale model rev eals that the amount of residual NAPL depends on the spreading coefficient and the water saturation. Furthermore, residual NAPL is history-dependent. At the continuum scale, a critical NAPL pressure head defines the transitio n from free, mobile NAPL to residual NAPL. Although the P-c-S relationships for water and total liquid are not independent in case of residual NAPL, t wo two-phase P-c-S relations can represent a three-phase residual system of P-c-S relations. A newly introduced parameter, referred to as the residual oil pressure head, reflects the mutual dependency of water and oil. Exampl e calculations show consistent behavior of the constitutive model. Entrapme nt and retention in the unsaturated zone cooperate to retain NAPL. Moreover , the results of our constitutive model are in agreement with experimental observations. (C) 2001 Elsevier Science B.V. All rights reserved.