A one-dimensional dual-porosity model has been developed for the purpose of studying variably saturated water flow and solute transport in structured soils or fractured rocks. The model involves two overlaying continua at the macroscopic level: a macropore or fracture pore system and a less permeable matrix pore system. Water in both pore systems is assumed to be mobile. Variably saturated water flow in the matrix as well as in the fracture pore system is described with the Richards' equation, and solute transport is described with the convection-dispersion equation. Transfer of water and solutes between the two pore regions is simulated by means of first-order rate equations. The mass transfer term for solute transport includes both convective and diffusive components. The formulation leads to two coupled systems of nonlinear partial differential equations which were solved numerically using the Galerkin finite element method. Simulation results demonstrate the complicated nature of solute leaching in structured, unsaturated porous media during transient water flow. Sensitivity studies show the importance of having accurate estimates of the hydraulic conductivity near the surface of soil aggregates or rock matrix blocks. The proposed model is capable of simulating preferential flow situations using parameters which can be related to physical and chemical properties of the medium. INTRODUCTION Porous media often exhibit a variety of heterogeneities, such as fractures, fissures, cracks, and macropores or interaggregate pores, and sometimes also show dynamic instabilities of the wetting front during infiltration. These microscopic structures or processes affect water and solute movement at the macroscopical level by creating nonuniform flow fields with widely different velocities. Such phenomena are often referred to as preferential flow [Beven, 1991]. They have been extensively studied for exploitation of fissured groundwater and petroleum reservoirs [Barenblatt et al., 1960; Warren and Root, 1963]. Similar problems are reported also for flow and transport in unsaturated fractured rocks [Evans and Nicholson, 1987; Pruess and Wang, 1987; Wang, 1991], for macroporous or structured field soils [Beven and Germann, 1982; Nielsen et al., 1986; Steenhuis and Parlange, 1991], and even for seemingly homogeneous coarse-textured soils [Hill and Parlange, 1972; Glass et al., 1989; Kung, 1990a, b; Baker and Hillel, 1991]. Preferential flow leads to an apparent nonequilibrium situation with respect to the pressure head or the solute concentration, or both [Brusseau and Rao, 1990; Wang, 1991], and severely limits our ability to predict flow and transport processes in undisturbed media. Flow and transport in structured porous media are frequently described using double-porosity (or dual) models. Such an approach assumes that the medium consists of two regions, one associated with the macropore or fracture network and the other with a less permeable pore system of soil aggregates or rock matrix blocks. Double-porosity models may b...

In heterogeneous structured soils, water and transported dissolved substances and suspended particles and colloids may under certain conditions bypass most of the soil porous matrix thereby creating nonequilibrium conditions in pressure heads and solute concentrations between preferential flow paths and the soil matrix pore region. Preferential flow severely limits the applicability of standard models for flow and transport that are mostly based on Richards' equation and the convection‐dispersion equation. A number of various model approaches have been proposed to overcome this problem. These models mostly try to separately describe flow and transport in preferred flow paths and slow or stagnant pore regions. Discrete fracture models are more frequently suggested in hydrogeology and often more empirically for cracked clay soils. The two‐domain approach assumes two interacting porous continua for either mobile‐immobile (compartment models) or mobile‐mobile pore systems for solute transport and for water movement. Such models were derived by rigorous “upscaling” methods (microstructure models), or by more empirically assuming two macroscopic scale systems. Representation of effective local (i.e., structural) geometry remains a problem when applying these models to soil systems. The dual‐permeability models differ in the description of flow in the preferential flow domain (i.e., either Richards' equation assuming capillarity or kinematic wave approach for gravity flow) and with respect to the mass‐transfer formulation (i.e., from pressure head– or saturation‐based first‐order type formulations to more complex nonlinear formulations or numerical solutions of the local flow equation). Despite the enormous progress that has been accomplished to improve both the modeling as well as the parameter determination, many challenges remain, in particular, how to capture dynamic soil structure effects to improve quantitative understanding and descriptions of preferential flow and transport processes.

Variably saturated water flow in a dual-porosity medium may be described using two separate flow equations which are coupled by means of a sink source term F•,, to account for the transfer of water between the macropore (or fracture) and soil (or rock) matrix pore systems. In this study we propose a first-order rate expression for Fw which assumes that water transfer is proportional to the difference in pressure head between the two pore systems. A general expression for the transfer coefficient aw was derived using Laplace transforms of the linearized horizontal flow equation. The value of aw could be related to the size and shape of the matrix blocks (or soil aggregates) and to the hydraulic conductivity K a of the matrix at the fracture/matrix interface. The transfer term Fw was evaluated by comparing simulation results with those obtained with equivalent one-and two-dimensional singleporosity flow models. Accurate results were obtained when K a was evaluated using a simple arithmetic average of the interface conductivities associated with the fracture and matrix pressure heads. Results improved when an empirical scaling coefficient yw was included in aw. A single value of 0.4 for 3% was found to be applicable, irrespective of the hydraulic properties or the initial pressure head of the simulated system. INTRODUCTIONDual-or double-porosity models, initially introduced to simulate single-phase flow in fissured groundwater reservoirs [e.g., Barenblatt et al., 1960], assume that a porous medium consists of two separate but connected continua. Of these, one continuum is associated with a system or network of fractures, fissures, macropores, or interaggregate pores, while the other continuum involves the porous matrix blocks or soil aggregates. Hence dual-porosity models usually involve two flow equations which are coupled by means of a sink/source term to account for water transfer between the pore systems.The dual-porosity concept has been popularly used to describe the preferential movement of water and solutes at the macroscopic scale, a phenomenon that is widely believed to occur in most natural (undisturbed) media [e.g., van Genuchten et al., 1990; Gish and Shirmohammadi, 1991; Wang, 1991]. A large number of double-porosity type models have been proposed to predict water flow in fractured reservoirs [Barenblatt et al., 1960; Warren and Root, !963; Duguid and Lee, 1977; Moench, 1984] or solute transport during both steady state flow [Coats and Smith, 1964; van Genuchten and Wierenga, 1976] as well as transient groundwater flow [Bibby, 198!]. Recently, attempts have been made to extend the concept to transient water flow and solute transport in variably saturated fractured rock formations and structured soils [Dykhuizen, 1987; Dudley et al., 1988; Peters and Klavetter, 1988; Jarvis et al., 1991; Chen and Wagenet, 1992a, b; Gerke and van Genuchten, 1993]. One of the most critical components of dual-porosity models is the source/sink term describing the exchange of water between the fracture and the matrix pore s...

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