Pipe Flow 1 Table of Contents


1 Introduction 
1.1 The many challenges involved in pipeline projects
1.1.1 History
1.1.2 Modern pipelines and their alternatives
1.1.3 Pipeline politics
1.1.4 What this book is about
1.2 Codes and specifications
1.3 A pipeline project’s different phases

1.3.1 Preliminary planning with feasibility study
1.3.2 Route selection
1.3.3 Acquisition of right-of-way
1.3.4 Various data collection
1.3.5 Pipeline design
1.3.6 Legal permits and construction
1.3.7 Commissioning and start-up
1.4 How pipe flow studies fit into a pipeline project, and which tools to
1.5 Different sorts of pipe flow models and calculations

1.5.1 Single-phase versus multi-phase models
1.5.2 Steady-state versus transient simulations
1.5.3 The flow simulation software’s different parts
1.6 Considerations when simulating pipe flow
1.6.1 General considerations
1.6.2 Hydrates and
1.6.3 Leak detection
1.6.4 Other features
 1.7 Commercially available simulation software
1.7.1 Single-phase pipe flow software
1.7.2 Steady-state multi-phase simulation programs
1.7.3 Transient simulation software
1.8 An example of what advanced pipe flow simulations can achieve

2 Pipe friction
   2.1 Basic theory
2.1.1 Introduction
2.1.2 Laminar flow
2.1.3 Turbulent flow
2.2 Simple friction considerations
2.3 Nikuradse’s friction factor measurements
2.4 What surfaces look like
2.5 The traditional Moody diagram
2.6 Extracting more from Nikuradse’s measurements
2.7 The AGA friction factor formulation
2.8 Towards a better understanding of the friction in turbulent pipe flow

2.8.1 Introduction about turbulence
2.8.2 Quantifying turbulence
2.8.3 Using Kolmogorov’s theory to construct a Moody-like diagram
2.8.4 Comparing the theoretical results with other measurements
2.8.5 Large surface imperfections dominate on non-uniform surfaces
2.8.6 Friction behaves the same way for all Newtonian fluids.
2.9 Practical friction factor calculation methods
2.9.1 The surface-uniformity based modified Moody diagram
2.9.2 Improving friction factor calculation speed
2.10 Fitting curves to measurements
2.11 Friction factor accuracy
2.12 Tabulated surface roughness data
2.13 Common friction factor methods
2.14 Transient friction
2.15 Other sorts of friction in straight, circular pipes
2.16 Friction factor summary

3 Friction in non-circular pipes
3.1 General
3.2 Partially-filled pipe
3.3 Rectangular pipe
3.4 Concentric annular cross-section
3.5 Elliptic cross-section

4 Friction losses in components
4.1 General
4.2 Valves
4.3 Bends
4.4 Welds joining pipe sections
4.5 Inlet loss
4.6 Diameter changes
4.7 Junctions

5 Non-Newtonian fluids and friction
5.1 Introduction
5.2 Pipe flow friction for power-law fluids
5.3 Pipe flow friction for Birmingham plastic fluids
5.4 Friction-reducing fluids

6 Transient flow
6.1 Mass conservation
6.2 Momentum conservation
6.3 Energy conservation
6.4 Examples to illustrate the conservation equations

6.4.1 Sloping liquid pipeline with steady-state flow
6.4.2 Horizontal gas pipeline with isothermal steady-state flow
6.4.3 Example: Gas pipeline cooling down after stop

7 Simplified liquid flow solution
7.1 Main principles
7.1.1 General
7.1.2 Involving fluid properties
 7.2 Solving the equations by the characteristics method
    7.2.1 Example: Instantaneous valve closure
7.3 Boundary conditions in the method of characteristics

7.3.1 Pipe with constant pressure at the inlet, closed outlet
7.3.2 Pipe with valve at the outlet
7.3.3 Valve located any other place than inlet or outlet
7.3.4 Inline centrifugal pump
7.3.5 Pump between reservoir and pipe inlet
7.3.6 Positive displacement pump
7.3.7 Junction
7.4 Instantaneous valve closure
7.4.1 Basic simulations
7.4.2 Some ways to check the simulations results manually
 7.5 Steady-state network analysis
7.5.1 General
7.5.2 Finding initial velocities using the steady-state characteristics method 182
7.5.3 Steady-state convergence criteria
7.5.4 Steady-state example
 7.6 Simulating transients in pipe networks, an example
7.7 Stability considerations

7.7.1 Frictionless flow
7.7.2 Flow with laminar friction
7.7.3 Turbulent flow
7.7.4 Some effects of the characteristic equations being nonlinear
7.8 Tracking the liquid
7.9 Checking simulation results
7.10 Advantages and limitations when using the method of characteristics

8 Heat exchange
8.1 General about heat through layered insulation
8.2 Heat transfer coefficient between fluid and pipe wall
8.3 Heat transfer coefficients for the pipe wall, coating and insulation layers
8.4 Heat transfer coefficient for outermost layer

8.4.1 Buried pipe
8.4.2 Above-ground pipe
8.5 The heat models’ limitations
8.5.1 Transient versus steady-state heat flow
8.5.2 Other accuracy considerations

9 Adding heat calculations to the characteristics method
9.1 The energy equation’s characteristic
9.2 Solving the energy equations using the explicit Lax-Wendroff’s method
9.3 Boundary conditions for the thermo equation

9.3.1 The problem with lack of neighboring grid-points at the boundary
9.3.2 Junctions, pumps, valves and other components
9.4 Determining secondary variables
9.5 Computing starting values
9.6 Stability considerations for the energy solution
9.7 Numerical dissipation and dispersion

9.7.1 How numerical dissipation and dispersion can affect the simulations
9.7.2 Easy ways to reduce numerical dissipation and dispersion
9.7.3 Modern, effective ways to counter dissipation and dispersion

10 Solving the conservation equations
10.1 Problem formulation
10.2 Some initial, simplified considerations
10.3 The conservation equations’ main properties
10.4 Selecting time integration and spatial discretization methods
10.5 How to account for friction and heat in the KT3 scheme
10.6 Calculating secondary from primary variables
10.7 Determining indirect fluid properties

11 Ghost cells
11.1 Some general considerations
11.2 Inserting ghost values: A simple method
11.3 An improved ghost cell approximation
11.4 Further ghost cell improvements
11.5 Computing state variables from flux variables

12 Boundary conditions
12.1 General
12.1.1 Boundary condition 1: Pressure source, inflowing fluid
12.1.2 Boundary condition 2: Pressure source, out-flowing fluid
12.1.3 Boundary condition 3: Mass flow source, in-flowing fluid
12.1.4 Boundary condition 4: Mass flow source, out-flowing fluid
12.2 Selecting boundary conditions in junctions
12.3 Other boundary conditions

13 Filling the ghost cells by using the boundary conditions directly
13.1 General philosophy
13.2 Mass flow source

13.2.1 Inflowing fluid
13.2.2 Outflowing fluid
 13.3 Pressure source

14 Simulation results and program testing
14.1 Simulating one of the world’s longest gas pipelines
14.2 Gas temperature in insulated pipelines
14.3 Simulating pipe rupture
14.4 How cooling affects the flow after shutdown
14.5 Comparing with other simulation programs

14.6 How to verify gas flow simulations, an overview
14.6.1 See if the integrations runs at all
14.6.2 Do the same checks as for liquid flow.
14.6.3 Checking the boundary and ghost cell approximations for steady-state flow
14.6.4 Checking the boundary and ghost cell approximations for transient flow
14.6.5 Check that the program uses correct fluid properties
14.6.6 Check the heat flow calculations manually
14.6.7 Increase the velocity until choking occurs
14.6.8 Things which may confuse result interpretation

15 Simplified models
15.1 General
15.2 Steady-state calculations
15.3 Fully transient isothermal model
15.4 Neglecting part of inertia for isothermal flow
15.5 Neglecting all terms to do with gas inertia

15.5.1 Model formulation
15.5.2 Numerical approximations
15.5.3 Important observations regarding neglecting the gas inertia