The post Energy in Fluid Mechanics: How to Ensure Physical Line and Operating Data Are Consistent first appeared on the ISA Interchange blog site.
This guest blog post is part of a series written by Edward J. Farmer, PE, ISA Fellow and author of the new ISA book Detecting Leaks in Pipelines. To download a free excerpt from Detecting Leaks in Pipelines, click here. If you would like more information on how to purchase the book, click this link. To read all the posts in this series, scroll to the bottom of this post for the link archive.
A common issue in a lot of pipeline work is ensuring the physical line data and operating data are consistent. This establishes confidence in the information about a project or situation, helps discern if a hypothetical situation can exist, or suggests that a broader view of a situation is appropriate. It also reminds the analyst of all the factors that pertain to a flow situation on a pipeline.
The Bernoulli equation looks at energy at selected locations along a pipeline. The analyst is free to choose these locations but must be sensitive to observability. Ends are always a good place to start. Often, the highest elevation point will be interesting. In some situations, the lowest points can be interesting. Points of delivery from the pipeline or injection into it may be interesting. Usually, work begins with some pipeline data and some operating data from specific sites along the line. Start analysis with those and ensure the core data the study will be based on is valid and consistent with the other known issues first.
For reasons that become apparent with some experience, Bernoulli and his follower, Euler, normally use a surrogate parameter for energy. This parameter is the “head” at the subject locations, reported in a length unit such as m for meters. Reported data is normally in typical engineering units such as velocity and pressure. Converting between these and head is fairly easy, albeit a bit tedious and obscure for newcomers. To efficiently summarize, the common transformations are:
Using the SI system:
Bernoulli’s (and Euler’s) development of these concepts was based on the idea of an isentropic pipeline, one in which the energy in the fluid itself, is constant. This presumes, for example, a constant temperature. Work since then introduces an internal energy term:
Essentially, the Bernoulli equation develops energy at the points for which the terms are calculated. The difference in energy between those points goes to the mechanical friction involved in moving the fluid. Fundamentally, the change in energy between location 1 and location 2 is dE = E2 – E1 m2/s2. This converts to a head difference of dH = dE/g meters.
The commonly used Darcy formula for friction flow loss, in head terms, is:
The head loss between points along the pipeline should match the computed head loss between them. When it doesn’t there is incentive to understand why.
There are usually at least three entities involved is obtaining pipeline data for these studies. The engineering department will normally know the characteristics of what was built and its current status. Normally they will have pump or compressor curves, data about the pipe and appetences as installed, and about the fluid as used in the design calculations.
The operators will know the current flows and pressures as well as the characteristics of the fluids in use. The business department will know what came into the system and what came out along with some useful data about energy consumed moving product. Hopefully the data needed to resolve a specific question or inquiry will match across all the sources.
If there are discrepancies, there may be some sort of observability issue with one or more of the involved groups and one or more of the involved places. Fluid mechanics, due to noise and measurement limitations may not always be as precise as some engineering undertakings in which everything is easily known in real-time to decimal places.
While a general Bernoulli analysis is not always adequate for resolving pipeline issues it will quickly, understandably, and simply establish where to look for more information or data. Sometimes the point-oriented concept motivates segmenting the analysis to concentrate on specific parts of the general pipeline.
The nature of the equations makes mathematical analysis, such as comparisons and sensitivity analysis, very straightforward and understandable. More precise analysis may involve continuous monitoring, special equipment, or investigating special situations. Keep an open mind and always thing back toward conditions that would produce or exacerbate the issue motivating the original request.
Book Excerpt + Author Q&A: Detecting Leaks in Pipelines
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What You Can Learn About Pipeline Leaks From Government Statistics
Is Theft the New Frontier for Process Control Equipment?
What Is the Impact of Theft, Accidents, and Natural Losses From Pipelines?
Can Risk Analysis Really Be Reduced to a Simple Procedure?
Do Government Pipeline Regulations Improve Safety?
What Are the Performance Measures for Pipeline Leak Detection?
What Observations Improve Specificity in Pipeline Leak Detection?
Three Decades of Life with Pipeline Leak Detection
How to Test and Validate a Pipeline Leak Detection System
Does Instrument Placement Matter in Dynamic Process Control?
Condition-Dependent Conundrum: How to Obtain Accurate Measurement in the Process Industries
Are Pipeline Leaks Deterministic or Stochastic?
How Differing Conditions Impact the Validity of Industrial Pipeline Monitoring and Leak Detection Assumptions
How Does Heat Transfer Affect Operation of Your Natural Gas or Crude Oil Pipeline?
Why You Must Factor Maintenance Into the Cost of Any Industrial System
Raw Beginnings: The Evolution of Offshore Oil Industry Pipeline Safety
How Long Does It Take to Detect a Leak on an Oil or Gas Pipeline?
Pipeline Leak Size: If We Can’t See It, We Can’t Detect It
An Introduction to Operations Research in the Process Industries
The Enigma of Process Knowledge
Energy in Fluid Mechanics: How to Ensure Physical Line and Operating Data Are Consistent
Source: ISA News