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Techniques and Methods, Book 6, Chapter A24 

#### 2008

*A product of the Ground-Water Resources Program*

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

**W. Barclay Shoemaker, Eve L. Kuniansky, 	Steffen Birk, Sebastian Bauer, and Eric D. Swain**

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|  |      Select an option:- Cover of report (1,178 KB)
- Main report (2,524 KB) |
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| **CONTENTS**Abstract*Chapter 1.* Introduction      1.1. Purpose and Scope      1.2. Previous Studies      1.3. Acknowledgments*Chapter 2.* Conduit Flow Process (CFP) Methodology      2.1. Reynolds Numbers and Limitations of Darcy´s Law for Porous Media      2.2. Coupling a Discrete Pipe Network with a Laminar Flow Model (CFPM1)            2.2.1. Laminar Flow Model            2.2.2. Pipe Network Geometry            2.2.3. Equations for Pipe Flow            2.2.4. Corrections for Flow in Partially Filled Pipes            2.2.5. Exchange of Water between the Pipe Network and Laminar Flow Model            2.2.6. Corrections to Exchange for Partially Filled Pipes      2.3. Computations of Turbulent Flow in Preferential Flow Layers (CFPM2)      2.4. Upper and Lower Critical Reynolds Numbers*Chapter 3.* Description of Conduit Flow Process (CFP) Programming      3.1. Integration of Simulation Modes      3.2. Conduit Flow Process (CFP) Program Flow            3.2.1. Conduit Flow Process (CFP) Allocate and Read Subroutine (CFP1AR)            3.2.2. Newton-Raphson Iterations            3.2.3. Exchange Subroutines            3.2.4. Conduit Pipe Recharge Subroutine            3.2.5. Subroutine for Solution of Conduit Flow Process Mode 2 (CFPM2) Heads            3.2.6. Conduit Flow Process (CFP) Budget Routines            3.2.7. Conduit Flow Process (CFP) Output Control Routines      3.3. MODFLOW-2005 Compatibility*Chapter 4.* Conduit Flow Process (CFP) Input Instructions      4.1. Name File      4.2. Conduit Flow Process (CFP) Input File      4.3. Conduit Output Control (COC) File      4.4. Conduit Recharge (CRCH) Package*Chapter 5.* Guidance on Assignment of Conduit Flow Process (CFP) Parameters      5.1. Parameter Guidance for the Conduit Flow Process Mode 1 (CFPM1)      5.2. Parameter Guidance for the Conduit Flow Process Mode 2 (CFPM2)*Chapter 6.* Conduit Flow Process (CFP) Example Problems      6.1. Conduit Flow Process Mode 1 (CFPM1) Example Problem      6.2. Conduit Flow Process Mode 1 (CFPM1) Input Files for Example Problem            6.2.1. Example CFPM1 Input File            6.2.2. Example CFPM1 Conduit Recharge (CRCH) Package            6.2.3. Example CFPM1 Conduit Output Control (COC) File            6.2.4. Results for CFPM1 Example Problem      6.3. Conduit Flow Process Mode 2 (CFPM2) Example Problem            6.3.1. Example CFPM2 Input File            6.3.2. Results for CFPM2 Example Problem      6.4. Conduit Flow Process Mode 3 (CFPM3) Example Problem            6.4.1. Example CFPM3 Input File            6.4.2. Results for CFPM3 Example Problem*Chapter 7.* Benchmark Testing*Chapter 8.* Selected References |

### Preface

This report is intended as a reference manual to explain:  (1) selected theoretical principles that govern laminar and turbulent ground-water flow, and (2) how these principles were integrated into MODFLOW-2005 to create the Conduit Flow Process (CFP). Users are advised to read each chapter in this report. Users interested in the motivation and theoretical principles represented in the CFP should read chapters 1 and 2. Chapter 3 documents how these theoretical principles were converted into subroutines and finite-difference approximations for integration into MODFLOW-2005. Chapters 4, 5, and 6 are most relevant for users interested in applying the CFP.  Specifically, chapter 4 documents the input instructions required for CFP simulations, chapter 5 provides guidance on assignment of values for parameters required for CFP simulations, and chapter 6 presents an example problem that demonstrates all of the CFP functionality.

The U.S. Geological Survey (USGS) has tested the accuracy of the CFP by designing and running many test problems. Despite our best efforts, errors may still exist. If users identify or suspect errors, please contact the USGS. Distribution of the CFP does not constitute any warranty by the USGS. Furthermore, no responsibility is assumed by the USGS for use or misuse of the  CFP computer program. The CFP computer program can be obtained at the Internet address  http://water.usgs.gov/software/ground_water.html. Updates may be made to both the CFP report and computer program, and users can download updates at the Internet address.

### 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.

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## Suggested Citation: 

> Shoemaker, W.B., Kuniansky, E.L., Birk, S., Bauer, S., and Swain, E.D., 2008, Documentation of a Conduit Flow Process (CFP) for MODFLOW-2005: U.S. Geological Survey Techniques and Methods, Book 6, Chapter A24, 50 p.

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