**1. Introduction**

Karst aquifer systems underlie approximately 10–20% of the Earth's landmass and supply potable water to nearly 25% of the world's population [1]. In the United States, karst carbo‐

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nate aquifers supplyalmost 52%of allbedrockaquiferwithdrawalsonayearlybasis [2, 3].Karst aquifers are typically characterized by relatively large void spaces and loose porous media, which make the karst aquifers to be the most productive aquifer systems in the world, for example, the Floridan aquifer in the USA [4]. The open and porous nature of karst aquifers, combined with the dissolution of joints and fractures within carbonates over time, generate complex subsurface conduit systems and dual‐permeability flow regimes [5]. Groundwater flow and solute transport processes in conduit networks are generally more rapid than that in the surrounding carbonate porous media due to significantly higher hydraulic conductivity and porosity in the conduit system [6, 7]. As a result,the water and solute interchanges between the conduit and matrix are particularly important in a dual‐permeability karst aquifer system. Karst aquifers are particularly vulnerable when one considers the problems of groundwater contamination [8]. During high‐flow events, contaminants in the conduit system can be rapidly transported through the aquifer or actively pushed into the carbonate matrix when the water pressure is high in the conduit system. The process is reversed during low‐flow events, and contaminants are slowly released from the surrounding matrix into the conduit system [9]. Therefore, groundwater contamination and seawater intrusion in a karst aquifer can persist for a long time because ofthe retention andrelease effect between the conduits andmatrixdomains [10, 11].

Laboratory experiments using physical models with artificial gypsum or sandbox analog were taken to simulate karst groundwater flow and solute transport [12]. Li [13] evaluated the solute transport and retention in a karst aquifer using two categories of laboratory experiments. Faulkner et al. [14] designed a sandbox laboratory experiment to simulate the interaction between conduit and porous medium domain. In addition to laboratory studies, many numerical models have been developed to study groundwater flow and solute transport in dual‐permeability systems, as well as chemical reaction and carbonate dissolution in karst aquifers [15]. For example, a limestone dissolution continuum model coupled with conduit flow was proposed to simulate groundwater flow and karst evolution [16]. Lauritzen et al. [17] coupled laminar flow and carbonate dissolution in two‐dimensional (2D) pipe networks to study groundwater flow and karst development in a limestone aquifer. Groves and Howard [18] used 2D pipe networks to simulate conduit development processes under laminar flow conditions at field scales, and the simulation method was later extended to turbulent flow by Howard and Groves [19]. Kaufmann and Braun [20] coupled a pipe network with a continuum system to study karst development and indicated that early karstification might be enhanced by the presence of a diffuse flow system.

The coupling of nonlinear or turbulent flow within the conduit network and Darcian laminar flow in the porous medium is a challenging issue in numerical simulation of a dual‐permea‐ bility karst aquifer [5, 21, 22]. Darcy equation of continuum groundwater flow is applicable for laminar flow in the porous medium that is linear to hydraulic gradient but is not accurate for nonlaminar or turbulent flow in the conduit. Some hybrid discrete‐continuum numerical models were developed to couple Darcian flow in the porous medium with nonlaminar channel flow in the conduit, such as carbonate aquifer void evolution (CAVE) [23, 24], MODFLOW‐CFPM1 [21] and CFPv2 [25, 26]. Those discrete‐continuum models were also applied and evaluated in a number of studies [22, 27–30].

The solute transport simulation in the discrete‐continuum model involves the coupling of 1D solute transport within the conduit network and the 2D/3D solute transport in the porous medium domain. MT3DMS is a widely used modular 3D model to simulate solute transport in a porous medium, which is based on the solution of groundwater flow from MODFLOW simulation [31]. Therefore, MT3DMS is only applicable for solute transport in porous medium aquifer [31]. Spiessl [32] and Spiessl et al. [33] modified the source code of MT3DMS and developed the reactive hybrid transport RUMT3D model. RUMT3D was coupled with CAVE to calculate groundwater flow in the conduits and then solve solute transport equations in the conduit and porous medium domains of a karst aquifer. Reimann et al. [34] enabled MOD‐ FLOW‐CFP simulation of unsaturated flow in conduits and water exchange between matrix and variably filled conduits. Furthermore, conduit‐associated drainable storage (CADS) was added in MODFLOW‐CFPM1 and fixed head‐limited flow boundary condition in Reimann et al. [25]. Based on those studies, a research version of CFPv2 has been recently developed by Reimann et al. [26] and used in Xu et al. [29] to simulate the flow of laminar and nonlaminar, as well as nitrate‐N transport in conduits and matrix with an updated UMT3D. The CFPv2 and UMT3D models were combined to calculate solute advective exchange between conduit and medium, as well as transport process within a porous medium by advection and disper‐ sion.
