This flow chart
provides an overview of your interaction with CYLEXPERT. The following example is taken from a
real-life situation. A steel pipe with a 3 inch (7.62 cm)
inner diameter was carrying a fluid with a density of about 0.93 g/cm3 and a viscosity
of 0.04 poise (g/cm/s) at a normal flow of about 2.5 ft/s (76.2 cm/s). The component
that could cause corrosion had a diffusion coefficient of about 1x10-6 cm2/s. The
rotating cylinder electrode used to model the system had a diameter of 0.75 in (1.91 cm).
An inordinate amount of corrosion was observed that seemed to increase during periods
when the fluid velocity increased. The question was raised if fluid flow influenced
corrosion in this system and, if so, would such corrosion be controlled by mass transfer.
The role that CYLEXPERT plays in this question is to provide guidance as to what rotation
rates should be used to assess if mass transfer controls corrosion in the pipe.
Detailed Instructions
CYLEXPERT is located at the web site www.argentumsolutions.com.
Enter CYLEXPERT. On the left hand side of each page including this one is a column
with the heading "Intelligent Tools". CYLEXPERT is the third icon listed. Double left
click on that icon. You are taken to an opening page which overlays the page you are on.
This page contains general information. When you have finished reading this information,
left click on the button labeled "Enter CYLEXPERT" at the top or bottom of the page.
This action takes you into the CYLEXPERT environment.
If you wish, read the "Overview" and "Instructions" to get a brief introduction to
CYLEXPERT and what you are asked to do. If you wish to go immediately to the "Instructions",
click on the word "Instructions". Note that you can change an entry at any time before
leaving this page.
Below the instructions you are asked to choose the type of geometry that you are examining.
You pick one of the 7 choices shown below. If you click on the geometry (in blue) you are shown a picture
of the geometry to help as a guide. In this case, the choice would be a straight pipe. Left click
on the "Next" button after the choice is made. If you make the wrong entry, select the "Start Over"
button, put in the correct entry, and then left click on the "Next" button.
As shown below for this example, "straight pipe with fully developed turbulent flow" has been
chosen.
In CYLEXPERT:
Please select the type of geometry. Then click on "Next" below. Straight Pipe with fully developed turbulent flow Non-circular ducts with fully developed turbulent flow Annulus with fully developed turbulent flow Curved pipe with fully developed turbulent flow Wall jet region of impinging jet on a flat plate
Downstream of flow expansion - region of maximum Sherwood Number Flat plate parallel to flow
A new page opens showing the picture of the geometry and a brief discussion of some
of the assumptions behind and limitations of the calculation for that geometry. In this case,
the picture is of a straight pipe and comments pertain to that geometry. After you scroll
past these two areas you are asked to fill in your name, affiliation, and email address.
This information will be kept internally and not shared. It is needed in case you contact Argentum Solutions
with questions.
In CYLEXPERT:
Straight Pipe With Fully Developed Turbulent Flow
The diameter to be used is the inside diameter (cm or in). The velocity is the rate of
flow in the pipe (cm/s or ft/s).
The concept of determining the equivalent rotation rate that would ensure equivalent mass
transfer rates in both the pipe and rotating cylinder electrode is built on the assumption
that fully developed mass transfer and hydrodynamic boundary layers are present in both
geometries. The estimate provided here assumes that your situation obeys that assumption.
One place that deviates from this assumption is the entrance region to a pipe. Both boundary
layers are developing here and the rate of mass transfer is higher. That rate decreases with
distance down the pipe finally reaching a constant value when the hydrodynamic boundary layer
becomes fully developed. In the case of liquids, though the entry region effects might be
observed at distances as high as 20 to 30 pipe diameters, most of the effect disappears at
distances of 5 to 10 diameters from the entrance.
Please enter the following information:
First Name:
Middle Initial:
Last Name:
Affiliation or Company Name:
Email Address:
In the next section, you fill in the parameters that CYLEXPERT needs to estimate
the range of rotation rates that may best model your system. The parameters you need
to have are the fluid density, fluid velocity, pipe inner diameter, fluid viscosity,
diffusion coefficient of component that is believed to cause corrosion, and diameter
of rotating cylinder electrode. You are also asked if the pipe is significantly roughened.
The observation is qualitative and if known will help to provide additional insight.
If not observed, make that choice. If the physical properties are not known, make an
educated guess. Note that some default values are provided but only use those values
if a judicious guess cannot be made. For example, the viscosity of water is about
0.01 poise, the density of water is about 1 g/cm3, and many diffusion coefficients
tend to lie in the range of 10-6 cm2/s to 10-5cm2/s.
You have your choice of metric or English units for a number of the
properties. When you are satisfied that you have entered all of the information
correctly, left click on "Run CYLEXPERT". If you make a mistake either type over the
error or left click on "Start Over" which erases all entries.
In CYLEXPERT:
Enter the fluid density (1 g/cm3 will be used if left blank)
g/cm3
Enter the fluid velocity
cm/s
ft/s
Enter the diameter of the pipe
cm
inches
Enter the absolute viscosity (0.01 g/cm-s will be used if left blank)
You can enter the number in exponential format, e.g. 1e-2
g/cm-s
lbm/ft-s
lbf-s/ft2
Enter the diffusion coefficient (10-5 cm2/s will be used if left blank)
You can enter the number in exponential format, e.g. 1e-5
cm2/s
Enter the outer diameter of the rotating cylinder
cm
inches
Is the pipe significantly roughened?
Yes
No
Not Observed
After you have clicked on "Run CYLEXPERT" a new screen appears with the calculated
range of rotation rates for assessing velocity sensitive corrosion and any additional
information that might be pertinent. For example, if the flow in the pipe as estimated
by the Reynolds number is not in the turbulent regime, the program will notify you
that it could not do the calculation because the rotating cylinder electrode should
not be used to model mass transfer under laminar flow conditions. If the range of
rotation rates is exorbitant and had to be changed to more reasonable values,
the output will make a note of that. In this case, the calculation led to a Reynolds
number of about 1500 and the range of rotation rates should be easily handled by
the rotating cylinder electrode. The range of rotation rates is estimated to be about
105 to 1058 rpm with a calculated value of 334 rpm.
In CYLEXPERT
This interactive program is being provided for test purposes only. Under
NO circumstances should any materials decisions be made based on the output you
receive.
This estimation tool provides an order of magnitude range of rotation rates spanning
an estimated "equivalent" rotation rate that might be used to assess the degree
of mass transfer control in the modeled geometry. The calculation estimates an
"equivalent" rotation rate of 334 rpm. The minimum range of rotation rates that
should be considered is 105 rpm to 1058 rpm. Very often, a wider range of rotation
rates is examined. Ensure that these ranges are handled safely by your experimental
set-up.
Below this section are provided two methods, "A" and "B", for assessing mass transfer
control. Method A is the simpler but less quantitative approach that could be used
when you lack concentration and physical property information. Method B requires
physical property and concentration information. It provides a more quantitative assessment
of the influence of mass transfer on corrosion. Clicking on either highlighted method
will take you to a description that is somewhat tailored to your particular situation.
Below the predictions, you are asked to submit your comments. Your name, affiliation,
and email address information will already appear based on your original input in Step 1.
You are asked to fill in the space with any comments and click on the "Submit" button.
This information is optional but feedback would be appreciated especially if the
prediction is contrary to your experience. You can return to any of the pages on
this web site by clicking the appropriate tab.
In CYLEXPERT:
The methods below are two approaches to assess if mass transfer influences corrosion
in your system. Method A is the simpler but less quantitative approach that could be
used when you lack concentration and physical property information. Method B requires
physical property and concentration information but provides a quantitative assessment
of the influence of mass transfer on corrosion.
Estimate the "corrosion rate" at several rotation rates, three rotation rates being the minimum.
Mass loss rate, corrosion current, or polarization resistance can be used as estimates of the corrosion
rate. The minimum range of rotation rates suggested by this estimator is 130 to 1304 rpm . Very often
the range tested is widened by the user. The fluid motion must be turbulent at all rotation rates and
the equipment must be able to handle the rotation rate. Generating this information over several days
can ensure that corrosion is at steady state.
Plot the logarithm of the corrosion rate estimate versus the logarithm of the rotation rate as measured
in rpm or in cm/s. This relationship should be fairly linear.
Perform a linear regression of the data points. Place the regression line on the same plot as the data
points. Examine the slope and the agreement of the regression with the measured data. Significant
curvature in the measured data relative to the regression may suggest additional processes are occurring
or the measurement is in error. Proceed on if measured and calculated values are in reasonable agreement.
If agreement between the regression and the measured values is poor ensure that your experimental set-up
and measurement technique and analysis are correct. If they are, other processes not measured by the
rotating cylinder electrode could be occurring.
If the slope of the regression lies between about 0.65 and 0.75, the corrosion rate is likely to
be significantly influenced or even controlled by mass transfer.
If the slope of the regression is much greater than 0.75, artifacts such as surface roughness
or particulate erosion could be affecting the results. Examine the electrode under magnification
for surface damage or surface roughening.
If the slope is much less than about 0.65 but is still greater than zero, mass transfer might
be having some influence but other factors may be detracting from fluid motion being the only
influence on the corrosion rate.
If the slope is close to zero, mass transfer is probably not having an effect.
Estimate the "corrosion rate" at several rotation rates, three rotation rates being the minimum.
Mass loss rate, corrosion current, or polarization resistance can be used for the measurement.
For this calculation, the measurement units must be converted to moles/s. The minimum range
of rotation rates suggested by the estimator is 130 to 1304 rpm. Very often the range tested
is widened by the user. The fluid motion must be turbulent at all rotation rates and the equipment
must be able to handle the rotation rate. Generating this information over several days can ensure
that corrosion is at steady state.
Estimate the mass transfer coefficient from the corrosion rate. This estimate requires use of
the following equation: where kcyl is the mass transfer coefficient, cm/s. |Cbulk-Csurf| is absolute value of the difference in concentration of
the rate limiting species between its concentration in the bulk fluid and its concentration at the
surface. One of the values is usually zero when the reaction is controlled by mass transfer.
The value that is not zero usually has to be measured. These concentrations are usually expressed
as mole/cm3. Acyl is the active area of the rotating cylinder, cm2. Corrosion Rate is the corrosion rate in the same units as the concentrations, moles/cm3.
The corrosion current is converted to these units by using the Faraday constant and the number of electrons
transferred for each molecule that reacts. If the rate is in mass loss per unit time, the equivalent weight
of the alloy is used for the conversion to moles per unit time.
Calculate the Sherwood Number, Shcyl by
The Sherwood number is dimensionless. Ensure that the units for each parameter are consistent and that
the Sherwood number as calculated is dimensionless.
Calculate the Schmidt Number, Sc, by
The diffusion coefficient can sometimes be found in physical property tables. Otherwise, a reasonable
value to assume is often in the range of 10-5 cm2/s. Ensure that the units for
each parameter are consistent and that the Schmidt number as calculated is dimensionless.
Calculate the Reynolds Number by
Ensure that the units for each parameter are consistent and that the Reynolds number as calculated is
dimensionless.
Divide the Sherwood number by the Schmidt number raised to the appropriate power for the rotating cylinder
electrode correlation you are using. The most widely accepted value of that power is 0.356.
Plot the logarithm of that calculation versus the logarithm of the Reynolds number.
For complete mass transfer control on a hydraulically smooth cylinder, the results should fall within the area labeled as such on the following plot:
Click for larger image
If the results fall well below the region but still have a slope, then there is probably some mass transfer influence but additional resistances to corrosion probably exist. If the results are significantly above the region, then surface roughness may be playing a role.
David C. Silverman, Ph.D. - Primary Consultant E-Mail:dcsilverman@argentumsolutions.com Phone: 314-576-3586 Fax: 314-754-9825 Address: The Argentum House
14314 Strawbridge Ct.
Chesterfield, MO 63017
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