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Fracture-Flow-Enhanced Matrix Diffusion in Solute Transport Through Fractured Porous Media

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Abstract

Over the past few decades, significant progress of assessing chemical transport in fractured rocks has been made in laboratory and field investigations as well as in mathematic modeling. In most of these studies, however, matrix diffusion on fracture–matrix surfaces is considered as a process of molecular diffusion only. Mathematical modeling based on this traditional concept often had problems in explaining or predicting tracer transport in fractured rock. In this article, we propose a new conceptual model of fracture-flow-enhanced matrix diffusion, which correlates with fracture-flow velocity. The proposed model incorporates an additional matrix-diffusion process, induced by rapid fluid flow along fractures. According to the boundary-layer theory, fracture-flow-enhanced matrix diffusion may dominate mass-transfer processes at fracture–matrix interfaces, where rapid flow occurs through fractures. The new conceptual model can be easily integrated with analytical solutions, as demonstrated in this article, and numerical models, as we foresee. The new conceptual model is preliminarily validated using laboratory experimental results from a series of tracer breakthrough tests with different velocities in a simple fracture system. Validating of the new model with field experiments in complicated fracture systems and numerical modeling will be explored in future research.

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Abbreviations

b :

Half aperture of fractures (m)

c :

Concentration (kg/m3)

c, c i :

Simulated concentration (kg/m3)

c * :

Measured concentration (kg/m3)

c f :

(Averaged) solute concentration across fractures (kg/m3)

c m :

Solute concentration of the matrix on the matrix block surface (kg/m3)

c o :

Constant fracture source solute concentration (kg/m3)

D :

Hydrodynamic dispersion coefficient along fractures (m2/s)

D E :

Effective enhanced matrix-diffusion coefficient (m2/s)

D m :

Free-solution molecular diffusion coefficient (m2/s)

D * :

Effective molecular diffusion coefficient (m2/s)

h c :

Mass-transfer coefficient at the fracture–matrix interface (m/s)

K f :

Distribution coefficient (m) on fracture surfaces, defined the solute mass adsorbed per unit area of fracture surface divided by solute concentration in solution

n :

Exponential

p :

Laplace operator

R f :

Fracture-face retardation coefficient

q c :

Mass-transfer flux at the fracture and matrix interface [kg/(s m2)]

v :

Mean-flow velocity in fracture (m/s)

\({\vec{v}}\) :

Fracture-flow velocity vector (m/s)

w i :

Weighting factor

α E :

Fracture-flow-enhanced dispersivity (m2-n/s1-n)

δ c :

Thickness of a concentration boundary (film) layer (m)

δ h :

Velocity boundary-layer thickness (m)

\({\phi}\) :

Porosity of the matrix

\({\phi}\) :

Objective function of Eq. 10

λ :

Decay constant (1/s)

τ :

Tortuosity of matrix porous media

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Authors and Affiliations

  1. Colorado School of Mines, Golden, CO, USA

    Yu-Shu Wu

  2. Florida State University, Tallahassee, FL, USA

    Ming Ye

  3. University of Waterloo, Waterloo, ON, Canada

    E. A. Sudicky

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  1. Yu-Shu Wu
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  2. Ming Ye
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  3. E. A. Sudicky
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Correspondence to Yu-Shu Wu.

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Wu, YS., Ye, M. & Sudicky, E.A. Fracture-Flow-Enhanced Matrix Diffusion in Solute Transport Through Fractured Porous Media. Transp Porous Med 81, 21–34 (2010). https://doi.org/10.1007/s11242-009-9383-4

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