A Network Pathway is made up of multiple “pipes”. The fact that these are referred to as pipes is not coincidental - each fracture network pipe has all the features and capabilities of the Pipe pathways discussed previously. In fact, Network pathways are effectively large collections of Pipe pathways. Like Pipe pathways, Network pathways contain only a single fluid medium (which is always, by definition, the Reference Fluid).
Network Pathways require specification of a fracture network, which can be entered by hand, but more likely would be generated by a discrete fracture network generation and flow simulation code. The fracture network identifies all of the pipes in the network, the manner in which they are connected, and each pipe's geometry and flow rate.
In addition, for each pipe in the fracture network, a fracture set is specified, which identifies the transport properties of the pipe (e.g., porous infill material, coating material, properties of matrix diffusion zones, etc.). The network of pipes can be very large (e.g., 100,000 pipes). This allows complex and realistic fracture systems to be simulated.
Warning: Solubility
constraints are not applied within Network pathways. (They are only
applied within Cells and Aquifers). Hence, if the concentration of a species entering a
Network pathway (e.g., via a boundary condition) exceeded the solubility limit,
the concentration leaving the Network could exceed the solubility
limit.
A schematic of a relatively small three-dimensional fracture network that could be simulated by GoldSim is shown below:
In addition to defining the fracture network, it is necessary to identify the mass flux links to and from the Network pathway (referred to as "sources" and "sinks", respectively), and specify the properties for all of the fracture sets referenced by the fracture network. Although there may be a very large number of “pipes” (100,000 or more), it is assumed that these can all be grouped into a relatively small (typically ten or less) number of fracture sets.
To facilitate representation of uncertainty in the fracture network connectivity and flow properties, you have the option to define a number of separate fracture networks and instruct GoldSim to randomly select one of these every realization.
The ability to solve Network pathways efficiently results from the fact that it is possible to develop a Laplace-transformed transfer matrix for an entire network of Pipe pathways by simple additions and multiplications of the transformed transfer matrices for each individual pathway. Once the network transfer matrix/matrices are developed, then the transport calculations for the network are no more time-consuming than for a single Pipe pathway. The only extra computational expense is the time required for the creation of the network transfer matrix at the beginning of the simulation. For even quite large networks (100,000 pipes or more), this time is not excessive.
The mathematical details of Network pathways are discussed in Appendix B of the Contaminant Transport Module User’s Guide.