Pressure drop model presentation april 19th
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Transcript of Pressure drop model presentation april 19th
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Pressure Drop Model and Experimental Variability
Plate and Frame Filter Press
Erin DurkeeYen Nguyen
Dalton Russell
CHE 4002-401 Chemical Engineering Laboratory I: Project III
Oklahoma State UniversityCoach Clint Aichele
Coach Mike ResetaritsCoach Russ Rhinehart
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Flow behaves like a transitional flow. Pressure drop model for the combined set of both laminar and
turbulent portions
Where:
a = 0.0484
b = 10.01
c = 0.0009
d = 5.47
p = 3.41
CONCLUSION
∆ 𝑃𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑=(𝑎+𝑏𝑁 )∗𝑄+(𝑐+
𝑑𝑁 𝑝 )∗𝑄𝑝
Apparatus Overall Diagram
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EXPERIMENTAL EQUIPMENT
Suspension Tank
Hand Wheel with Spindle
Overall System
Pumpoutlet Thermometer Pumpoutlet Pressure Gauge
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EXPERIMENTAL EQUIPMENT
Bypass Stop Valve Pipe Diaphragm Valve Filterinlet Pressure Gauge
Filteroutlet Flow MeterFilter Plate Arrangement
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EHS & LP Environmental – water is the only component used
Health – no health hazards
Safety – wear standard lab clothing and safety glasses – slipping hazard due to water
Loss Prevention – use minimal amount of resources necessary
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THEORY Pressure drops through two different zones in the filter press:• the in-pipe zone :
• laminar• turbulent • transitional
• porous medium of the filter paper: • laminar • turbulent• transitional ∆ 𝑃=∆ 𝑃𝑝𝑖𝑝𝑒+∆ 𝑃𝑝𝑜𝑟𝑜𝑢𝑠
(A sketch to illustrate the two different zones.)
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THEORY Darcy-Weisbach equation:
Where: • f: Darcy friction factor• L and D: length and inside diameter of the pipeline• ρ: density of water• Q: flow rate of water through the unit
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THEORY: In-pipe zone:
Porous medium zone:
Where:• c, d are turbulent flow unknown constants• N: the number of filter papers used, or the number of
split flows during the filtering process
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Theory : Laminar Flow Data from the Moody diagram (Munson):
Plug back into the Darcy-Weisbach equation:
Poiseuille’s law:
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THEORY: In-pipe zone:
Porous medium zone:
Where: • a, b are laminar flow unknown constants
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THEORY Laminar only:
Turbulent only:
Combined Flow:
∆ 𝑃 𝑙𝑎𝑚𝑖𝑛𝑎𝑟=(𝑎+ 𝑏𝑁 )∗𝑄
∆ 𝑃𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑=(𝑎+𝑏𝑁 )∗𝑄+(𝑐+
𝑑𝑁 𝑝 )∗𝑄𝑝
∆ 𝑃 𝑡𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡=(𝑐+𝑑𝑁2 )∗𝑄2
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DATA PROCESSING Flow rate:
Where:• V1, V2 : initial and final readings of volume in gallons
• t1, t2 : initial and final readings of time in minutes
• 6.309*10-5 : unit conversion for the flow rate (Q) from gal/min to m3/s
𝑄=( 6.309∗10−5 )∗𝑉 2−𝑉 1
𝑡2−𝑡 1
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DATA PROCESSING Data model:
Where:• : specific weight of water • (z3-z2) : change in elevation
• KL=7: minor loss coefficient for the water meter equipment
• Re ≤ 2100: ; Re ≥ 4000:
𝑃2=𝛾 (𝑧 3− 𝑧2+[ 𝑓 𝐿𝐷 +𝐾 𝐿 ] 8𝑄2
𝑔𝜋 2𝐷4 )Sketch to illustrate the points (2) and (3)
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EXPERIMENTAL PLANDAY 1 – PRELIMINARY TRIALS
N plates
6 psig
Record Flow Rate in 1 min
Calculate P2
Repeat with new filter papers
*N = 8, 12, and 16
Number of Plates:
Inlet Pressure (P1): 9 psig 12 psig
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EXPERIMENTAL PLANDAY 2 – VARIABILITY AND MODEL TESTING
14 plates
Proper Orientation
Record Flow Rate in 1 min
Calculate P2
Number of Plates:
Inlet Pressure Range (P1): 3 – 12 psig
Random Orientation
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EXPECTATION The value of the outlet pressure P2 should be less than 0 psig.
• a, b, c, d, and p are not negative • Laminar flow coefficients: if a ≠ 0, then c = 0 • Turbulent flow coefficients: if b ≠ 0, then d = 0
The graph of pressure drop ∆P vs. flow rate Q should be:• increasing linear line if laminar flow only• positive increasing quadratic curve if turbulent only
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POLYMATH - NONLINEAR REGRESSION
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POLYMATH REPORT
Laminar Turbulent Combined
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RESULTS The combined
flow model best described the data:
Where:
a = 0.0484 c =
0.0009
b = 10.01d
= 5.47
p = 3.41 ∆ 𝑃𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑=(𝑎+
𝑏𝑁 )∗𝑄+(𝑐+
𝑑𝑁 𝑝 )∗𝑄𝑝
3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.64.505.005.506.006.507.007.508.008.509.009.50
10.0010.5011.0011.5012.0012.5013.00
Pressure drop vs. Flow rate when N=8
Data Model
Laminar Model
Turbulent Model
Combined Model
Flow Rate Q (gal/min)
P1-P2 (psig)
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VARIABILITY OF MEDIUM
Proper Orientation Random Orientation
4.5 5 5.5 6 6.5 7 7.5 8 8.5 93.003.504.004.505.005.506.006.507.007.508.008.509.009.50
10.0010.5011.00
Pressure drop vs. Flow rate when N=14
Process Model
Data Model
Flow rate Q (gal/min)
P1-P
2 (p
sig)
4.2 4.7 5.2 5.7 6.2 6.7 7.2 7.7 8.2 8.73.003.504.004.505.005.506.006.507.007.508.008.509.009.50
10.0010.5011.00
Pressure drop vs. Flow rate when N=14
Data Model
Process Model
Flow rate Q (gal/min)
P1-P
2 (p
sig)
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STATISTICAL TEST
Preliminary Trials
Two-tailed t-test: Passed
R-lag-1 test: Did not pass
large negative
Proper Orientation
Two-tailed t-test: Passed
R-lag-1 test: Did not pass
large positive
Random Orientation
Two-tailed t-test: Did not pass
R-lag-1 test: Did not pass
large positive
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RESIDUAL PLOTS
Preliminary Trials Proper Orientation
1 2 3 4 5 6 7 8 9 10
-0.50
-0.30
-0.10
0.10
0.30
0.50
0.70
0.90
Plot of Residuals when N=14
Trials
Res
idua
ls
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PROPAGATION OF UNCERTAINTY Data model:
ε(p1) (psig) ε(z3) (m) ε(z2) (m) ε(L) (m) ε(D) (m) ε(V2) (m3) ε(V1) (m3) ε(t2) (min) ε(t1) (min)
4.00 0.0010 0.0010 0.0010 0.0010 0.0004 0.0004 0.0083 0.0083
1 -1.42E+00 1.42E+00 -5.63E-02 7.65E+01 -1.79E+05 1.79E+05 2.72E+03 -2.72E+03
1 -1.42E+00 1.42E+00 -5.88E-02 8.03E+01 -1.84E+05 1.84E+05 2.85E+03 -2.85E+03
1 -1.42E+00 1.42E+00 -6.13E-02 8.41E+01 -1.88E+05 1.88E+05 2.99E+03 -2.99E+03
1 -1.42E+00 1.42E+00 -8.61E-02 1.23E+02 -2.26E+05 2.26E+05 4.36E+03 -4.36E+03
1 -1.42E+00 1.42E+00 -9.21E-02 1.32E+02 -2.34E+05 2.34E+05 4.70E+03 -4.70E+03
εΔP, 0.95
81.02
83.14
85.27
105.09
109.65
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PROPAGATION OF UNCERTAINTY
Result • Average 95% probable errors: ε∆P , 0.95 = 136.89• Two sigma limit : 2σ = 0.88
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DISCUSSION
Model works well in the range of:• N=8 up to 14 plates• Low to medium-high flow rate
At a very high flow rate (when control valve shows PI1 ≈ 2 bar):• Accurate inlet pressure readings P1 were hard to obtain
• Residuals between data model and processing model increase• Data started showing outliers, model does not fit data well
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REFERENCES1. Munson, Bruce R., Ted H. Okiishi, Wade W. Huebsch, and Alric P.
Rothmayer. Fundamentals of Fluid Mechanics, 7th edition. Jefferson City: John Wiley & Sons, Inc, 2013. 400-410, 416-431. Print.
2. Rhinehart, R. R. (2016). Lessons on Data Analysis and Model and Procedure Validation. Oklahoma State University.
3. Venugopal, Vidhya. Standard Operating Procedures: Experiments in Plate and Frame Filter Press. Oklahoma State University.
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Pressure Drop Model and Experimental
VariabilityPlate and Frame Filter Press
Erin Durkee
Yen Nguyen
Dalton Russell
Conclusion:
QUESTIONS?
∆ 𝑃𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑=(0.0484 +10.01𝑁 )∗𝑄+(0.0009+
5.47𝑁3.41 )∗𝑄3.41
Units:• ∆Pcombined (psig)• Q (gal/min)