An analytical model for solute transport through a water-saturated single fracture and permeable rock matrix

Abstract

[1] The problem of solute transport through a water-saturated single fracture in a permeable rock matrix is examined using an analytical modeling approach. A closed-form analytical solution is obtained that accounts for transverse and longitudinal advective transport in the fracture and matrix and transverse diffusion in the matrix. The solution also accounts for both diffusive and advective solute exchange between the fracture and matrix and a general solute source position in either the fracture or matrix. The novel features are the incorporation of advective transport in the matrix and a general source position into a closed-form solution for the solute-transport problem. Examples of the solution behavior are presented, which demonstrate the effects of matrix advection in combination with advection along the fracture, transverse diffusion in the matrix for solute release in the fracture and matrix. A semianalytical solution in the form of a superposition integral is also derived that includes these transport features, plus independent levels of longitudinal diffusion and dispersion in the matrix and fracture, respectively. Examples are presented that include advective transport in the fracture and matrix, longitudinal and transverse diffusion in the matrix, longitudinal dispersion in the fracture, as well as solute release from the fracture and matrix. An approximate criterion is proposed to evaluate the significance of longitudinal diffusion and dispersion relative to longitudinal spreading caused by fracturematrix interaction.

A modelling investigation of solute transport in permeable porous media containing a discrete preferential flow feature

“…In recent decades, considerable research attention has been given to the transport of solutes in aquifers of low-permeability rock matrices containing PFFs, where the transport of solutes occurs primarily via advection and dispersion within the PFF, and exchanges between PFFs and the rock matrix occur by molecular diffusion (e.g. Grisak and Pickens, 1981;Sudicky and Frind, 1982;Himmelsbach et al, 1998;Bense et al, 2013, Gassiat et al, Rubin andBuddemeier (1996), Rubin et al (1997), Odling and Roden (1997), Sonnenborg et al (1999) and Houseworth et al (2013) . Birkhölzer et al (1993a;1993b ) presented an analytical model to describe advection-dominated solute transport (i.e.…”

“…Further experimental and theoretical work was recommended to test the range over which the EPM approach might be valid. Houseworth et al (2013) obtained a closed-form analytical solution for solute transport during steady-state saturated flow in a single PFF embedded within a porous, permeable rock matrix. Unlike existing analytical solutions, Houseworth et al (2013) incorporated lateral matrix diffusion, and flows through both the matrix and PFF.…”

“…Houseworth et al (2013) obtained a closed-form analytical solution for solute transport during steady-state saturated flow in a single PFF embedded within a porous, permeable rock matrix. Unlike existing analytical solutions, Houseworth et al (2013) incorporated lateral matrix diffusion, and flows through both the matrix and PFF. Their study considered the case where matrix diffusion dominates in comparison to matrix dispersion, and hence they did not provide insight into the effect of a PFF on a solute plume in a matrix that is subjected to both advection and dispersion.…”

Application of analytical diffusion models to outcrop observations: Implications for mass transport by fluid flow through fractures

“…The mass transfer and the form of redox fronts associated with diffusion and fluid flow in rock fractures was investigated by analytical modeling [ Grisak and Pickens , ; Grisak et al ., ; Tang et al ., ; Sudicky and Frind , ; Rubin et al ., ; Park et al ., ; Wörman et al ., ; Houseworth , ; Sidborn and Neretnieks , ; Houseworth et al ., ; Rajaram and Arshadi , ], experimental work [ Hölttä et al ., ; Trivedi and Babadagli , ; Hatiboglu and Babadagli , ], and numerical modeling [ Steefel et al ., ; Spiessl et al ., ; MacQuarrie et al ., ; Vujevic and Graf , ; Watanabe and Kolditz , ]. Ortoleva et al .…”

“…Furthermore, redox front characteristics help to understand pollutant transport in porous [Cribbin et al, 2014] or fractured rocks [Akagawa et al, 2006]. The reaction chemistry associated with redox fronts helps to constrain the dynamics of pollutants exchange from the highpermeability fracture to the surrounding low-permeability rock-matrix [Mutch et al, 1993;Mazurek et al, 1996;Rubin et al, 1997;Brown et al, 1998;Banwart et al, 1999;Molinero and Samper, 2006;Greer et al, 2010;Wu et al, 2010;Houseworth et al, 2013;Vujevic and Graf, 2015]. This is also of interest in the context of two-phase flow and DNAPL movement from fractures into the adjacent rock matrix [Esposito and Thomson, 1999].…”