A new numerical method of considering local longitudinal dispersion in single fractures Zhihong Zhao 1, * ,† , Lanru Jing 1 , Ivars Neretnieks 2 and Luis Moreno 2 1 Department of Land and Water Resources Engineering, Royal Institute of Technology, Sweden 2 Department of Chemical Engineering and Technology, Royal Institute of Technology, Sweden SUMMARY The solutions of advection–dispersion equation in single fractures were carefully reviewed, and their relationships were addressed. The classic solution, which represents the resident or flux concentration within the semi-infinite fractures under constant concentration or flux boundary conditions, respectively, describes the effluent concentration for a finite fracture. In addition, it also predicts the cumulative distribution of solute particle residence time passing through a single fracture under pulse injection condition, based on which a particle tracking approach was developed to simulate the local advection–dispersion in single fractures. We applied the proposed method to investigate the influence of local dispersion in single fractures on the macrodispersion in different fracture systems with relatively high fracture density. The results show that the effects of local dispersion on macrodispersion are dependent on the heterogeneity of fracture system, but generally the local dispersion plays limited roles on marodispersion at least in dense fracture network. This trend was in agreement with the macrodispersion in heterogeneous porous media. Copyright © 2013 John Wiley & Sons, Ltd. Received 2 June 2012; Revised 17 January 2013; Accepted 2 March 2013 KEY WORDS: local dispersion; macrodispersion; single fracture; discrete fracture network; solute transport; particle tracking method 1. INTRODUCTION Mass transport through fracture media is an important issue in many energy, engineering and environmental applications such as underground nuclear waste repositories, CO 2 sequestration, contaminant migration and mineral forming process e.g. [1–4]. During the modeling of solute transport in fractured rocks, it is commonly argued whether the local dispersion in single fractures is negligible at the macro-scale of fracture network. Some authors assert that macrodispersion in fracture networks predominates and hides completely the local individual-scale dispersion, so the latter could be neglected in solute transport simulation in fractured rocks e.g. [5–8]. This assumption can considerably simplify and speed up the solute transport simulation, but it probably gives rise to some potential errors, particularly when dealing with pollutant transport e.g. [9]. However, the impacts of local dispersion in single fractures on solute transport through fracture network were shown in other literature such as Rasmuson and Neretnieks[10] and Kapoor and Gelhar [11, 12]. To the authors’ best knowledge, both arguments are possible, but the key issue that remains poorly understood is that the significance of effects of local dispersion on macroscopic transport largely depends on the geometrical and flow conditions. de Dreuzy et al. [13] and Zhao et al. [14] found *Correspondence to: Zhihong Zhao, Department of Geological Sciences, Stockholm University, SE-106 91, Sweden. † E-mail: zhihong.zhao@geo.su.se Copyright © 2013 John Wiley & Sons, Ltd. INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. 2014; 38:20–36 Published online 26 April 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nag.2191