Documentation of a Conduit Flow Process (CFP) for MODFLOW-2005

Abstract

This report documents the Conduit Flow Process (CFP) for the modular finite-difference ground-water flow model, MODFLOW-2005. The CFP has the ability to simulate turbulent ground-water flow conditions by: (1) coupling the traditional ground-water flow equation with formulations for a discrete network of cylindrical pipes (Mode 1), (2) inserting a high-conductivity flow layer that can switch between laminar and turbulent flow (Mode 2), or (3) simultaneously coupling a discrete pipe network while inserting a high-conductivity flow layer that can switch between laminar and turbulent flow (Mode 3). Conduit flow pipes (Mode 1) may represent dissolution or biological burrowing features in carbonate aquifers, voids in fractured rock, and (or) lava tubes in basaltic aquifers and can be fully or partially saturated under laminar or turbulent flow conditions. Preferential flow layers (Mode 2) may represent: (1) a porous media where turbulent flow is suspected to occur under the observed hydraulic gradients; (2) a single secondary porosity subsurface feature, such as a well-defined laterally extensive underground cave; or (3) a horizontal preferential flow layer consisting of many interconnected voids. In this second case, the input data are effective parameters, such as a very high hydraulic conductivity, representing multiple features. Data preparation is more complex for CFP Mode 1 (CFPM1) than for CFP Mode 2 (CFPM2). Specifically for CFPM1, conduit pipe locations, lengths, diameters, tortuosity, internal roughness, critical Reynolds numbers (NRe), and exchange conductances are required. CFPM1, however, solves the pipe network equations in a matrix that is independent of the porous media equation matrix, which may mitigate numerical instability associated with solution of dual flow components within the same matrix. CFPM2 requires less hydraulic information and knowledge about the specific location and hydraulic properties of conduits, and turbulent flow is approximated by modifying horizontal conductances assembled by the Block-Centered Flow (BCF), Layer-Property Flow (LPF), or Hydrogeologic-Unit Flow Packages (HUF) of MODFLOW-2005. For both conduit flow pipes (CFPM1) and preferential flow layers (CFPM2), critical Reynolds numbers are used to determine if flow is laminar or turbulent. Due to conservation of momentum, flow in a laminar state tends to remain laminar and flow in a turbulent state tends to remain turbulent. This delayed transition between laminar and turbulent flow is introduced in the CFP, which provides an additional benefit of facilitating convergence of the computer algorithm during iterations of transient simulations. Specifically, the user can specify a higher critical Reynolds number to determine when laminar flow within a pipe converts to turbulent flow, and a lower critical Reynolds number for determining when a pipe with turbulent flow switches to laminar flow. With CFPM1, the Hagen-Poiseuille equation is used for laminar flow conditions and the Darcy-Weisbach equation is applied to turbulent flow conditions. With CFPM2, turbulent flow is approximated by reducing the laminar hydraulic conductivity by a nonlinear function of the Reynolds number, once the critical head difference is exceeded. This adjustment approximates the reductions in mean velocity under turbulent ground-water flow conditions.