FluidFlow
RESULTS VERIFICATION
© Flite Software NI Ltd
1 INTRODUCTION 3
2 Liquid Calculations 4
2.1 Case 1: Pressure drop of Water in a Turbulent Pipe Flow. 4
2.2 Case 2: Pressure drop of Oil in a Turbulent Pipe Flow. 6
2.3 Case 3: Three Reservoir System. 8
2.4 Case 4: Crane Example 4-15 (Technical Paper No. 410). 10
2.5 Case 5: Gravity Fed System. 12
2.6 Case 6: Fire Piping System. 16
2.7 Case 7: Fire Sprinkler System. 18
2.8 Case 8: Pumping Facility. 20
2.9 Case 9: 106 Mile Piping System. 23
2.10 Case 10: 1 Mile Oil Piping System. 25
3 Compressible Flow 27
3.1 Case 1: Piped Gas Flow Between Two Known Pressures. 27
3.2 Case 2: Piped gas flow with known flow and inlet conditions 28
3.3 Case 3: Pressure drop sensitivity to varying incremental pipe lengths 30
3.4 Case 4: Flow Through a Broken Pipe. 32
3.5 Case 5: Calculating Gas Flowrate given a Known Pressure Drop across a Pipe. 33
3.6 Case 6: Estimating Pressure Drop along a Pipe Transporting Superheated Steam. 34
3.7 Case 7: 100 kM Buried Seabed Pipe Heat Transfer Calculation. 35
3.8 Case 8: Nitrogen Flow through a Pipeline. 37
3.9 Case 9: Relief Valve Sizing (Hydrocarbon System). 39
3.10 Case 10: Compressor System. 41
4 Two-Phase (Liquid-Gas) Systems. 43
4.1 Case 1: System Pressure Loss Example 43
4.2 Case 2: Two-Phase Steam System. 45
4.3 Case 3: Two-Phase Textbook Example (Constant Quality). 47
4.4 Case 4: Flow Pattern Map (Air-Water). 50
5 Non-Newtonian Slurries 52
5.1 Case 1: Pressure Gradient in a Pipeline Transporting Chalk Slurry. 52
5.2 Case 2: Sewage System Pressure loss 54
5.3 Case 3: Pressure Gradient for Herschel Bulkley Sewage Model. 56
5.4 Case 4: Food Process Plant – Power Law Fluid. 58
5.5 Case 5: Mayonnaise Process Piping. 60
6 Settling Slurries 61
6.1 Case 1: Transport of Coal Slurry. 61
6.2 Case 2: Effect of Particle Size and Grading on Sand Transport. 63
6.3 Case 3: Heterogeneous Slurry Flow. 65
6.4 Case 4: Pump Sizing for Heterogeneous Slurry. 67
6.5 Case 5: Mica Case Study. 69
6.6 Case 6: 800M Vertical Pipe - Heterogeneous Slurry. 71
7 Pulp & Paper 73
7.1 Case 1: Pulp & Paper System (Chemical Pulp). 73
1. INTRODUCTION
FluidFlow software is designed to allow the modelling of fluid behaviour within complex piping systems, and accurately predict how the system will work for a given set of design conditions. The software uses a number of well-established models and correlations to solve the piping systems.
The purpose of this document is to verify the accuracy of FluidFlow against published design examples from the available literature on the subject. To that end, a number of case studies are detailed below, in which the published data is compared to the solutions provided by FluidFlow. Each case will be accompanied by a brief description, and a summary of the design inputs used in the calculations.
The cases have been categorised by fluid type as follows;
- Liquids (Incompressible Flow).
- Gases (Compressible Flow).
- Two-Phase Liquid-Gas Flow.
- Non-Newtonian/Non-Settling Slurry Flow/Pulp & Paper Stock.
- Settling Slurry Flow.
The results generated by FluidFlow for liquids, gases, two-phase fluids and slurries are rigorously tested and verified against published data and real-world operating systems on a continuous basis. An extensive library of Quality Assurance test models are also installed with the software.
As FluidFlow is continuously undergoing development, each new version of the software is benchmarked using the above procedures.
FluidFlow has been used successfully in industry since it was first launched 1984. The software has undergone extensive development since first launched ensuring the product is up to date, includes the very latest solution technology and offers engineers a fast and effective design simulation tool.
Quality Assurance is an integral part of our business ethic. From our software design approach through to our released product, FluidFlow is developed to the highest quality and standard.
Flite Software Ltd is an ISO9001:2008 registered company.
2. Liquid Calculations
2.1 Case 1: Pressure drop of Water in a Turbulent Pipe Flow.
Reference: Fluid Flow Handbook, 2002, McGraw-Hill, Jamal Saleh, Pg 8.13, Example 8.2.
Description: 500 gallons per minute at 68°F water flows in a horizontal 3” schedule 40 commercial steel pipe. Determine the pressure loss in psi and head loss per 1000ft of flow distance.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Friction Factor |
0.0184 |
0.018469 |
|
Reynolds Number |
514000 |
514975 |
|
Head loss (fluid ft per 1000ft length) |
526 |
530 |
|
Pressure Drop (Psi) |
227 |
229 |
Commentary:
The handbook results for Reynolds number have been rounded to 514000 whereas FluidFlow has calculated the value accurately. This will have a subtle effect on the calculated friction factor and therefore, the overall calculated pressure loss result. It is therefore considered that the FluidFlow result is highly accurate.
2.2 Case 2: Pressure drop of Oil in a Turbulent Pipe Flow.
Reference: Fluid Flow Handbook, 2002, McGraw-Hill, Jamal Saleh, Pg 8.15, Example 8.3.
Description: 120 barrels per hour of an oil flows in a horizontal commercial steel pipe with an I.D. of 3.068 in. Determine the pressure loss in psi and head loss per 1000ft of flow distance. The oil has a SG = 0.9, and kinematic viscosity = 10 cSt.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Friction Factor |
0.034 |
0.033784 |
|
Reynolds Number |
7826 |
7823 |
|
Head loss (fluid ft per 1000ft length) |
27.5 |
27.3 |
|
Pressure Drop (Psi) |
10.7 |
10.7 |
Commentary:
The results compare very favourably, with error margins of 0.8 percent or less. This can be attributed to the rounding up of the friction factor in the published data.
2.3. Case 3: Three Reservoir System.
Reference: Hydraulics of Pipeline Systems, 2000, CRC Press LLC, Larock, Jeppson and Watters, Pg 26, Example 2.7.
Description: Three reservoirs of increasing elevation are connected, with a flow demand out of the system at the connection point of 0.06m3/s. The elevations of the 3 reservoirs are 100m, 85m, and 60m.
The highest reservoir is connected via a 2000m long pipe of I.D. 300mm. The second highest is connected via a 1500m long pipe of I.D. 250mm. The lowest reservoir is connected via a 3000m long pipe of I.D. 250mm. Pipe roughness for all pipes is 0.5mm.
Determine the flows into or out of each of the reservoirs.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow from highest reservoir (m3/s) |
0.1023 |
0.1022 |
|
Flow from middle reservoir (m3/s) |
0.02 |
0.02 |
|
Flow into lowest reservoir (m3/s) |
0.0622 |
0.06 |
Commentary:
The results compare very well with the hand calculation.
2.4. Case 4: Crane Example 4-15 (Technical Paper No. 410).
Reference: Crane Technical Paper No. 410, Example 4-15, Page 4-9.
Description: Determine the total discharge head requirement for the pumped system featuring a lift check valve and gate valve over a differential elevation of 120M.
All pipes shall be 3 inch Schedule 40 and the pump design flow rate shall be 400 l/min.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Duty Pressure Rise (m fluid) |
127 |
127.2 |
Commentary:
The results compare very well with the hand calculation.
2.5. Case 5: Gravity Fed System.
Reference: Piping Calculations Manual, Example 1.19, Page 48.
Description: A gravity fed system consists of a 16 inch, 3000 ft long pipeline with a supply tank elevation of 500 ft and a discharge tank elevation of 150 ft. Calculate the flow rate through this flow system using a Hazen Williams Coefficient of 130.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow Rate (usgpm) |
15484 |
15505 |
Commentary:
The FluidFlow results when using the Hazen Williams correlations compare very well with the hand calculation.
This example was then updated to use a fixed friction factor of 0.02.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow Rate (usgpm) |
12949 |
12940 |
Commentary:
The FluidFlow results when using a fixed friction factor compare very well with the hand calculation.
This example was then updated to use the Moody relationship.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow Rate (usgpm) |
16186 |
16019 |
Commentary:
The slight difference in results can be attributed to the rounding of values in the handbook for Reynolds Number and friction factor. Overall, the results compare well.
2.6. Case 6: Fire Piping System.
Reference: Piping Calculations Manual, Example 2.11, Pg 102.
Description: A 234mm diameter steel pipe is used to transport water from a fire pump to a fire protection water distribution piping system. Calculate the friction factor and pressure gradient at a flow rate of 250 m3/h. Assume a pipe roughness of 0.05mm. Use Moody to calculate the pressure loss and determine the pump pressure required if the pipe length is 198m. The delivery point is located at a height of 50 m.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Friction Factor |
0.0162 |
0.0162 |
|
Pressure Gradient (kPa/m) |
0.0897 |
0.0900 |
|
Pump Pressure (kPa) |
508 |
508 |
|
Pipe Velocity (m/s) |
1.61 |
1.61 |
Commentary:
The results compare very well with the hand calculation.
2.7. Case 7: Fire Sprinkler System.
Reference: Piping Calculations Manual, Example 2.17, Pg 128.
Description: A sprinkler system for a small warehouse has three branch pipes with four sprinkler heads, each spaced at 12ft apart. The branch lines are spaced 15ft apart and connect to a riser pipe 20ft high from the fire pump. The riser pipe is 2 inch schedule 40. The branch lines are 1 inch schedule 40 except for the section from the top of the riser to the first sprinkler on each branch line, which is 1.5 inch schedule 40. All sprinklers have a 0.5 inch orifice with K = 5.6. Use a Hazen Williams C factor of 100 for all pipes. Calculate the flow through each sprinkler.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Inlet Static Pressure (psig) |
83.16 |
81.56 |
|
Total Flow Rate (usgpm) |
319.5 |
319.5 |
|
Sprinkler 1 Flow Rate (usgpm) |
37.65 |
36.68 |
|
Sprinkler 1 Pressure (psig) |
45.20 |
42.90 |
|
Sprinkler 2 Flow Rate (usgpm) |
27.19 |
26.45 |
|
Sprinkler 2 Pressure (psig) |
23.58 |
22.30 |
|
Sprinkler 3 Flow Rate (usgpm) |
21.65 |
21.08 |
|
Sprinkler 3 Pressure (psig) |
14.95 |
14.18 |
|
Sprinkler 4 Flow Rate (usgpm) |
20 |
19.47 |
|
Sprinkler 4 Pressure (psig) |
12.76 |
12.09 |
Commentary:
The FluidFlow results for this entire system compare very well with the hand calculation. This system is based on using the Hazen Williams friction loss approach.
2.8. Case 8: Pumping Facility.
Reference: Piping Calculations Manual, Example 3.12, Pg 152.
Description: A concrete pipe with a 2 M I.D. is used to transport water from a pumping facility to a storage tank 5 km away. Calculate the pressure loss in kPa/km due to friction at a flow rate of 34,000 m3/h. Use the Hazen Williams equation with a C factor of 140. If a delivery pressure of 400 kPa must be maintained at the delivery point and the storage tank is at an elevation of 200 M above that of the pumping facility. Calculate the pressure required at the pumping facility at the given flow rate.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure Gradient (kPa/km) |
24.38 |
24.24 |
|
Pressure Required at Pump (kPa) |
2483 |
2481 |
Commentary:
The FluidFlow results for this entire system compare very well with the hand calculation. This system is based on using the Hazen Williams friction loss approach.
2.9. Case 9: 106 Mile Piping System.
Reference: Piping Calculations Manual, Example 1.26, Pg 67.
Description: A 29 inch I.D. pipeline with a total length of 106 miles is used to transport 10000 gal/min with intermediate deliveries at C & D of 2000 and 3000 gal/min respectively. At point E, 4000 gal/min of water is injected into the pipeline so that a total of 9000 gal/min is delivered to the terminus at B at 50 psi. Calculate the pressure loss in each section of pipework using a Hazen Williams C factor of 120 whilst taking into account changes in system elevation. The system elevations details are as follows;
A = 100ft, B = 340ft, C = 180ft, D = 150ft & E = 280ft.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure Loss (psi) (Pipe Section A – C) |
149.96 |
149.18 |
|
Pressure Loss (psi) (Pipe Section C – D) |
163.81 |
163.09 |
|
Pressure Loss (psi) (Pipe Section D – E) |
32.49 |
32.33 |
|
Pressure Loss (psi) (Pipe Section E – B) |
144.76 |
144.18 |
Commentary:
The FluidFlow results for this entire system compare very well with the hand calculation. This system is based on using the Hazen Williams friction loss approach.
FluidFlow has also generated the HGL/EGL for the system as follows;
2.10. Case 10: 1 Mile Oil Piping System.
Reference: Piping Calculations Manual, Example 6.16, Pg 335.
Description: A petroleum oil with SG 0.85 and 10 cSt viscosity flows through a 15.5 inch I.D. pipeline at a flow rate of 4000 bbl/h. The absolute roughness of the pipe is estimated to be 0.002 in. Calculate the pressure loss due to friction in a mile of pipe length using the Colebrook-White equation.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Friction Loss (psi/mile) |
11.01 |
11.02 |
|
Pipe Velocity (ft/s) |
4.76 |
4.76 |
Commentary:
The FluidFlow results for this entire system compare very well with the hand calculation over a distance of 1 mile for this oil transportation line.
3. Compressible Flow
3.1 Case 1: Piped Gas Flow Between Two Known Pressures.
Reference: Fluid Flow Handbook, 2002, McGraw-Hill, Jamal Saleh, Pg 9.12, Example 9.3
Description: Find the air flow rate in a 4 inch I.D. pipe with an upstream pressure of 150 psia and downstream pressure of 65 psia. The flow mis assumed adiabatic at an average temperature of 70oF. The pipe length is 100 ft.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow Rate (lb/s) |
20.6 |
20.6 |
Commentary:
The software results are an exact match with the hand calculation. Note, FluidFlow does not assume gas ideality as the software solves for real gas conditions using an equation of state for incremental pipe lengths. This ensures the highest level of accuracy. We would therefore expect some level of difference in calculated results.
3.2. Case 2: Piped gas flow with known flow and inlet conditions
Reference: Fluid Flow Handbook, 2002, McGraw-Hill, Jamal Saleh, Pg 9.13, Example 9.4.
Description: Calculate the pressure drop for natural gas pipe with 50 MMSCFD (75% Methane, 20% Ethane, 5% Propane). The pipe is 1 mile long, with an I.D. of 10 inches. The gas inlet conditions are 185 psig and 70 oF.
FluidFlow Model
Calculated Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure Loss (psi) |
19.89 |
22.75 |
Commentary:
The text book example uses a modified Darcy equation to generate a linear plot of pressure loss against flow rate, with 6 points. The published data result stated above has then been taken from that linear approximation. FluidFlow uses the Duxbury method and takes into account density changes of the gas as it flows along the pipeline. Considering this pipeline is 1 mile in length, the density changes will have an effect on the overall result. The software also takes into account the J-T effect.
Considering the above, we would expect the results to differ with FluidFlow returning a high level of accuracy.
3.3 Case 3: Pressure drop sensitivity to varying incremental pipe lengths
Reference: Fluid Flow Handbook, 2002, McGraw-Hill, Jamal Saleh, Pg 9.25, Example 9.9.
Description: 5 kg/s of gas flows in a pipe with 6 inches inside diameter. The pipe inlet pressure is 100 psia and the inlet temperature is 100 oF. The pipe length is 500 ft and the pipe roughness may be assumed to be 0.0018 in. Find the exit pressure and temperature using pipe incremental lengths of 1, 10 and 50.
FluidFlow Model
Sample Pipe Input
Result Comparison:
|
Description |
No of Nodes |
Published Data |
FluidFlow Results |
|
Exit Pressure (psia) |
1 |
N/A |
88.45 |
|
Exit Pressure (psia) |
10 |
87.47 |
88.44 |
|
Exit Pressure (psia) |
50 |
87.40 |
87.51 |
Commentary:
The purpose of the text book exercise is to demonstrate an increase in accuracy when the pipeline is broken up into smaller segments for calculation purposes. The results comparison demonstrates that FluidFlow provides a good estimation of exit pressure with only one pipe used in the model, with increasing accuracy as more nodes are added. The designer can make an engineering decision on the number of nodes to be modelled to give satisfactory model accuracy. It is noted that there is a law of diminishing returns – indeed the text book example states that in this case, any further increase in nodes over 100 will yield negligible improvement.
For further comparison, values for pressure drop and velocity in the pipe broken down into 10 increments is tabulated below. It is noted that temperature has not been compared as only a very basic temperature calculation has been carried out in the handbook and insufficient data is available to complete an accurate calculation.
Result Comparison:
|
|
Handbook |
|
FluidFlow |
|
||
|
Pipe Increment |
Inlet Pressure (psia) |
Pressure Drop (psi) |
Velocity (ft/s) |
Inlet Pressure (psia) |
Pressure Drop (psi) |
Velocity (ft/s) |
|
1 |
100 |
1.1808 |
114.008 |
100 |
1.0881 |
115.865 |
|
2 |
98.82 |
1.2069 |
115.096 |
98.90 |
1.0994 |
117.017 |
|
3 |
97.61 |
1.2194 |
116.232 |
97.80 |
1.1117 |
117.320 |
|
4 |
96.39 |
1.232 |
117.405 |
96.68 |
1.1244 |
119.667 |
|
5 |
95.16 |
1.2451 |
118.617 |
95.54 |
1.1376 |
121.062 |
|
6 |
93.92 |
1.2586 |
119.87 |
94.40 |
1.1513 |
122.507 |
|
7 |
92.66 |
1.2727 |
121.167 |
93.24 |
1.1654 |
124.004 |
|
8 |
91.38 |
1.2872 |
122.51 |
92.06 |
1.1801 |
125.558 |
|
9 |
90.1 |
1.3023 |
123.903 |
90.87 |
1.1967 |
127.172 |
|
10 |
88.79 |
1.318 |
125.348 |
89.66 |
1.2147 |
129.159 |
|
Total |
87.47 |
12.52 |
|
88.44 |
11.47 |
|
3.4. Case 4: Flow Through a Broken Pipe.
Reference: Internal Flow Systems, 2nd Ed., 1996, BHR Group, D.S.Miller, Pg 175, Example 1.
Description: A safety assessment indicates that the most likely impact induced failure will occur at a certain point of a 0.1m2 CSA pipe carrying air from a pressure vessel. Assuming a double ended failure occurs (i.e. a complete and clean break) find the initial flow rate from the vessel for the following air conditions in the vessel; P = 930 kPa a, T = 290 K, and pipe friction coefficient of 0.012.
FluidFlow Model
System Inlet Data
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Exit Flow (kg/s) |
152 |
158 |
Commentary:
The results compare reasonably well. The calculation procedure carried out in the text book is described as “reasonably accurate”. We would expect FluidFlow to yield a more accurate result due to the method and rounding up of values in the text book.
5. Case 5: Calculating Gas Flowrate given a Known Pressure Drop across a Pipe.
Reference: Internal Flow Systems, 2nd Ed., 1996, BHR Group, D.S.Miller, Pg 183, Example 7.
Description: A natural gas pipeline of 0.334 m internal diameter, 100 km long, operates with a pressure drop of 65 bar. If the inlet pressure is 80 bar, estimate the flow rate in kg/s.
FluidFlow Model
System Inlet Data
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow (kg/s) |
33.2 |
35.3 |
Commentary:
The results compare well. The discrepancy in the result can be explained in the value of viscosity used in the calculations. The text book proposes a value of 10-5 Pa s, while FluidFlow uses an extrapolated value of 12.5 x 10-5 Pa s.
3.6. Case 6: Estimating Pressure Drop along a Pipe Transporting Superheated Steam.
Reference: Handbook of mechanical engineering calculations, 2nd Ed., 2006, McGraw-Hill, Tyler G Hicks, Pg 8.15.
Description: Determine the pressure loss in 510 ft of 4in steel pipe containing fittings of equivalent length 40ft. The schedule 40 piping conveys 5850 kg/h of superheated steam at 275.8 kPa & 177 °C.
FluidFlow Model
System Inlet Data
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure Loss (kPa) |
274.9 |
274.1 |
Commentary:
The results correlate extremely well. The text book used published steam tables to arrive at the result, while FluidFlow calculated the value from the design inputs. In fact, the fluid is defined as water in FluidFlow however, the software automatically determines that it is in gas phase based on the design pressure and temperature conditions and applies the appropriate correlations.
7. Case 7: 100 kM Buried Seabed Pipe Heat Transfer Calculation.
Reference: Gas/dp Software.
Description: In this example system, we have an offshore natural gas production platform exporting gas at 80oC via a 100km, 20” buried sea-bed pipeline. The pipeline is modelled in three sections as follows;
- Pipe segment exposed to air (no coating).
- Pipe segment exposed to sea coated in 3mm polyethylene.
- Pipe segment running along the sea bed coated with 1.5mm PVC and 75mm concrete.
The overall heat transfer coefficients for each pipe segment have been established from the table of typical values. The air and sea temperatures used in the example are 10oC and 5oC degrees respectively.
This heat transfer example is one of many FluidFlow verification examples and the calculated results have been compared to those available from the software package known as “Gas/dp” which is discontinued. Note, the results produced by the “Gas/dp” program were in the past widely accepted as having a high level of accuracy.
FluidFlow Model
FluidFlow Results
System Design Data:
Volumetric Flow Rate: 6000000 m3/day.
Upstream Pressure: 70 Bar a.
Upstream Temperature: 80°C.
Result Comparison:
|
Software |
In Temp (oC) |
Out Temp (oC) |
In Density (kg/m3) |
Out Density (kg/m3) |
In Pressure (bara) |
Out Pressure (bara) |
In Velocity (m/s) |
Out Velocity (m/s) |
Heat Transfer (kW) |
|
FluidFlow |
80 |
3.5 |
48.98 |
49.06 |
70 |
50.07 |
6.2 |
6.24 |
8980 |
|
Gas dp |
80 |
4.16 |
50.18 |
50.9 |
70 |
50.99 |
6.1 |
5.97 |
9511 |
Commentary:
Considering this is an example of gas flow across a considerable length of pipework which include heat transfer, the results correlate extremely well. Note, FluidFlow does not assume gas ideality but calculates for real gas conditions providing a high level of accuracy.
Note, an illustration of the density and velocity profile of the gas as it flows along the pipe length are outlined below.
The above graphs provide a classic representation of a density and velocity profile along a gas pipeline. Note, how the gas velocity decreases initially as the gas cools before it then increases as the gas expands along the pipeline.
3.8. Case 8: Nitrogen Flow through a Pipeline.
Reference: Pipe Flow – A Practical & Comprehensive Guide (AIChE).
Description: In this example, the reference literature uses Turton’s equations to determine the flow of nitrogen through a 4 inch schedule 40 pipeline over a distance of 100ft. The inlet pressure and temperature condition is 100 psia and 530 R and the outlet pressure is 84.056 psi a.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow (lb/s) |
10.00002 |
10 |
Commentary:
The results correlate extremely well, and with rounding applied can be considered to yield an identical result.
3.9. Case 9: Relief Valve Sizing (Hydrocarbon System).
Reference: API 520 RP, Example 3.6.2.2, Pg 44.
Description: As well as modelling specific manufacturer’s relief valves in piping systems, FluidFlow allows you to automatically size relief valves and bursting disks for liquids, gases and two-phase systems to API & ISO standards.
This hand calculation for auto-sizing a relief valve is for a butane & pentane hydrocarbon system taken from the API standard. The design flow rate is given as 53500 lb/h, the relieving temperature and pressure is 348 Kelvin and 75 psi g respectively and the back pressure is given as 14.7 psi a (or 1 atm).
The permitted accumulation is 10 % and the relieving pressure is 97.2 psi a. A discharge coefficient of 0.975 has been used and the calculated relief orifice size is 3179mm2.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Relief Valve Size (mm2) |
3179 |
3148.8 |
Commentary:
The results correlate extremely well. The size is just slightly different and this can be attributed to a number of reasons;
- The physical properties (molecular weight etc) of the FluidFlow gas mixture is slightly different to that used in the API standard as the FluidFlow mixture is based on a mixture ratio of 50-50. Note, the API standard doesn’t describe the % of butane or pentane in the mixture.
- FluidFlow does not assume gas ideality but solves for real gas conditions using an equation of state (and you can choose from three).
- The API standard considers the RV in isolation whereas it has been solved in this system with two pipes connected.
Note that, when using the API pressure loss model, FluidFlow suggests the next standard size orifice available which you can then consider in your system design.
3.10. Case 10: Compressor System.
Reference: Piping Calculations Manual, Example 5.3, Pg 262.
Description: A compressor is used to pump air through a pipeline at 150 psig and a flow temperature of 75 °F. The compressor is rated at 600 standard ft3/min (SCFM). Calculate the airflow rate under actual conditions in actual ft3/min (ACFM).
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Actual Flow Rate (ACFM) |
55.1 |
55 |
Commentary:
The results correlate extremely well.
4. Two-Phase (Liquid-Gas) Systems.
4.1. Case 1: System Pressure Loss Example
Reference: Fluid Flow Handbook, McGraw-Hill, Example 11.3.
Description: Calculate the pressure loss in a two-phase system pipeline (50.8mm diameter) which features an air input of 240.7 m3/h at 26.6 °C and water at 5.677 m3/h at 26.6 °C.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure loss (kPa/m) |
5.15 |
5.78 |
Commentary:
The FluidFlow results correlate extremely well with that provided by the Fluid Flow Handbook.
2. Case 2: Two-Phase Steam System.
Description: This system comprises of 121m of 10 inch Schedule 40 steel pipework. The system inlet condition is known to be 477735.11 lb/hr steam at 313.40 o F and the outlet condition is 68.88 psi a with a vapor quality of 0.013143.
The task is to calculate the system and determine the inlet fluid pressure & temperature and outlet vapor quality using FluidFlow.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Inlet Pressure (psia) |
84.78 |
83.39 |
|
Inlet Temperature (oF) |
313.4 |
314.9 |
|
Outlet Vapor Quality |
0.013143 |
0.0123 |
Commentary:
The results calculated by FluidFlow are extremely close to that provided by the customer for the operating system. Comparing the software result for that of a real-world two-phase operating system provides useful validation.
4.3. Case 3: Two-Phase Textbook Example (Constant Quality).
Description: A liquid-gas mixture is to flow in a line having a 358ft of level pipe and three vertical rises of 10ft each and one vertical rise of 50ft. evaluate the type of flow and expected pressure drop.
Fluid Data:
|
Description |
Flow (lb/h) |
Density (lb/ft3) |
Density (kg/m3) |
Viscosity (cP) |
|
Liquid |
1000 |
63.0 |
1009 |
1.0 |
|
Gas |
3000 |
0.077 |
1.23 |
0.00127 |
Pipework: 3 Inch, Schedule 40 Stainless Steel (I.D. 3.068 in).
Relative Pipe Roughness: 0.000587.
Note: The literature calculation is based on the gas having a viscosity of 0.00127 cP and assumes gas ideality. For convenience, based on the gas having a density of 1.23 kg/m3,
the model has been developed using air as the gas. It should therefore be noted that air has a viscosity of 0.018 cP and based on pressure and temperature in addition to the engineering conditions which apply, air density is 2.51 kg/m3 at the system inlet. Furthermore, FluidFlow does not assume gas ideality but calculates for real gas conditions.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
|
|
FluidFlow Results |
||||||
|
Description |
Published Data |
Friedel |
Chisholm Baroczy |
Lockhart Martinelli |
Drift Flux |
Beggs & Brill |
MSH |
HEM |
|
In Stag Pressure (psia) |
--- |
30.06 |
29.44 |
25.92 |
25.71 |
30.05 |
29.45 |
21.48 |
|
Out Stag Pressure (psia) |
--- |
14.7 |
14.7 |
14.7 |
14.7 |
14.7 |
14.7 |
14.7 |
|
Total System Pressure Drop (psi) |
15.8 |
15.36 |
14.74 |
11.22 |
11.01 |
15.35 |
14.75 |
6.78 |
|
Liquid Velocity (ft/s) |
0.086 |
0.087 |
0.087 |
0.087 |
0.087 |
0.087 |
0.087 |
0.087 |
|
Gas Velocity (ft/s) |
211 |
205.5 |
205.5 |
205.5 |
205.5 |
205.5 |
205.5 |
205.5 |
Commentary:
The literature calculation is based on the gas having a viscosity of 0.00127 cP and assumes gas ideality. For simplicity, the model has been developed using air which has a viscosity of approx. 0.018 cP at 15 °C. The density of the air is also quite different as the hand calculation has assumed air density to be 1.23 kg/m3 when it's closer to 2.51 kg/m3. This will therefore have a slight effect on the calculated results.
The “hand” calculation is based on ideal gas conditions. FluidFlow does not assume gas ideality but solves for REAL gas conditions and hence, provides more accurate results.
Based on the above, it is considered that the results provided by FluidFlow correlate well with the hand calculation and offer an accurate reflection of the system operating conditions. It is also considered that the Friedel correlation may be best suited for this particular application owing to the combination of both vertical and horizontal pipes.
4.4 Case 4: Flow Pattern Map (Air-Water).
Reference: Fluid Flow Handbook, McGraw-Hill, Example 11.1.
Description: Determine the superficial liquid and gas velocities and the flow regime for a 2 inch pipeline transporting air & water at a flow rate of 0.08023 kg/s and 1.5713 kg/s respectively. The temperature of the air and water shall be 80 oF.
FluidFlow Model
FluidFlow Flow Pattern Map
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow Regime |
Annular Mist |
Annular Mist |
|
Liquid Superficial Velocity (m/s) |
33 |
31.47 |
|
Gas Superficial Velocity (m/s) |
0.778 |
0.73 |
Commentary:
The FluidFlow results based on the Drift Flux Correlation correlate well with that provided by the Fluid Flow Handbook. The viscosity of water and air in the handbook are 0.81 and 0.01812 cP whereas FluidFlow uses 0.857 and 0.01845 cP. This will contribute to a slight difference in results.
5. Non-Newtonian Slurries
5.1. Case 1: Pressure Gradient in a Pipeline Transporting Chalk Slurry.
Reference: Flow of Fluids in Piping Systems, 2002, Butterworth Heinemann, R.P King, Pg 141, Example 5.4.
Description: Calculate the pressure gradient due to friction along a 5.7 cm pipe when the chalk slurry flows at a rate of 2.23 x 10-3 m3/s. Refer to the text book for slurry properties.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure Gradient (Pa/m) |
215.8 |
223.3 |
|
Pipe Velocity (m/s) |
0.874 |
0.874 |
Commentary:
The results compare well. Variations are to be expected when dealing with non-Newtonian slurries, due to the error element associated with best fitting a curve to the available data points.
5.2. Case 2: Sewage System Pressure loss
Description: Calculate the pressure loss along a 200mm pipe with a length of 10M when the sewage slurry flows at a rate of 78.54 kg/s.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure Loss (Pa) |
6061 |
6068.6 |
Commentary:
The results calculated by FluidFlow compare favourably with that provided by the Fluid Flow Handbook.
5.3. Case 3: Pressure Gradient for Herschel Bulkley Sewage Model.
Reference: Flow of Fluids in Piping Systems, 2002, Butterworth Heinemann, R.P King, Pg 134, Example 5.3.
Description: Calculate the flow rate of laterite slurry delivered in a 7cm diameter pipe line. System inlet pressure is 110 Kpa a and outlet pressure is 100 Kpa a. Refer to the text book for slurry properties.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Flow Rate (m3/s) |
0.0226 |
0.0245 |
Commentary:
The results calculated by FluidFlow compare well with that provided by the Fluid Flow Handbook. The slight difference in results can be attributed to the subtle difference in Reynolds numbers.
5.4. Case 4: Food Process Plant – Power Law Fluid.
Reference: Rheological Methods in Food Process Engineering – James F. Steffe, Pg 152, Example 2.12.6.
Description: High fructose corn syrup (power law) shall be pumped from an input tank to an output tank at elevations of 0 & 2.5 m respectively. The system has a 0.0348 m diameter pipeline with a design flow rate of 1.97 kg/s resulting in an average velocity of 1.66 m/s. The fluid density is 1250 kg/m3. The system includes a plug valve and a strainer which has a pressure drop of 100 kPa. Determine the friction losses in the system where K = 5.2 Pa s and n = 0.45.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Velocity (m/s) |
1.66 |
1.66 |
|
Pressure Drop (kPa) |
265 |
264 |
Commentary:
The results calculated by FluidFlow offer a high level of accuracy when compared with that provided by the Steffe Handbook.
5. Case 5: Mayonnaise Process Piping.
Reference: Introduction to Food Process Engineering – P.G. Smith, Pg 112, Example 6.15.
Description: Determine the pressure drop for a piping system transporting mayonnaise (power law fluid) at a flow rate of 0.002 m3/s. The mayonnaise has a behaviour flow index of n = 0.31 and K = 27.5 Pa s.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure Drop (Pa) |
282000 |
282403 |
Commentary:
The results calculated by FluidFlow offer a high level of accuracy when compared with that provided by the Food Process Engineering Handbook.
6. Settling Slurries
FluidFlow provides five correlations for settling slurry pipelines as follows;
- Durand.
- WASC (Wilson, Addie, Sellgren, Clift).
- Wasp.
- Four-Component Model.
- Liu Dezhong.
The following section provides an outline of just some calculation verification examples completed using FluidFlow.
6.1. Case 1: Transport of Coal Slurry.
Reference: Slurry Transport Using Centrifugal Pumps 3rd Edition, 2006, Springer, Wilson, Addie, Sellman and Addie, Pg 404, Case Study 6.2.
Description: Coal is to be transported through a pipe with D = 17.3 inches and fw = 0.013 mm at a solids concentration Cvd = 0.25. The coal has the following properties – Ss = 1.4, 
, and 
. The particle sizes yield a d50 of 2.0mm and d85 of 2.8mm. Calculate the maximum limit of deposition velocity, Vsm.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Vsm (ft/s) |
6.2 |
6.33 |
|
Friction Loss Gradient (ft water/ft pipe) |
0.0313 |
0.03123 |
Commentary:
The results correlate extremely well, and with rounding applied can be considered to yield the same answer.
6.2. Case 2: Effect of Particle Size and Grading on Sand Transport.
Reference: Slurry Transport Using Centrifugal Pumps 3rd Edition, 2006, Springer, Wilson, Addie, Sellman and Addie, Pg 401, Case Study 6.1.
Description: This study investigates the accuracy of FluidFlow with varying particle size distributions. The slurry is pumped through a pipe with D = 25.6 inches at 20% solids concentration by volume. D50 is 0.70mm and D85 is 1.00mm. The slurry is assumed to be travelling at a velocity of 20.7 ft/s in the pipe.
FluidFlow Model
Pipe Input Data
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Friction Loss Gradient (ft water/ft pipe) Case 1 |
0.0612 |
0.0630 |
|
Friction Loss Gradient (ft water/ft pipe) Case 2 |
0.0653 |
0.0691 |
|
Friction Loss Gradient (ft water/ft pipe) Case 3 |
0.0589 |
0.0589 |
Commentary:
The results compare favourably, with variation between the two results sets attributed to rounding up of values in the published data.
6.3. Case 3: Heterogeneous Slurry Flow.
Reference: Flow of Fluids in Piping Systems, 2002, Butterworth Heinemann, R.P King, Pg 106, Example 4.7.
Description: Calculate the pressure gradient due to friction when a slurry of sand in water having D50 = 0.63 mm and D85 = 0.74 mm is transported through a 20.3 cm horizontal pipe with a solids fraction of 0.138. The density of the sand is 2650 kg/m3 and the slurry flows at 3 m/s. The coefficient of friction between the settled solids and the pipe wall is 0.44.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Reynolds Number |
6.09 x 105 |
6.11 x 105 |
|
Friction Loss (kPa/m) |
1.14 |
1.094 |
Commentary:
The results compare favourably. The text book example uses a water viscosity value of 0.001 Pa s while FluidFlow extrapolates a viscosity value based on the temperature of the water in the slurry. A temperature of 20oC has been assumed, which gives a viscosity value (0.0015 Pa s) close to that used in the text book.
6.4. Case 4: Pump Sizing for Heterogeneous Slurry.
Reference: Warman Slurry Handbook, 2009, Pg 32.
Description: A heavy duty slurry pipe is required to transport 65 tph of sand (d50 of 0.211 mm) with a S.G. of 2.65 in a slurry with 30% concentration by weight of solids. The pipeline is 100 M long, 6 inches in diameter, and has an elevation difference of 20 M. The pipeline also includes 5 x 90o long radius bends.
FluidFlow Model
FluidFlow Results
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pump Duty |
176.2m3/h @ 28.53 m water |
176.2m3/h @ 29.49 m water |
|
Deposition Velocity (m/s) |
2.3 |
2.3 |
Commentary:
The results correlate extremely well, with negligible difference between the two results. In both cases, the Durand method has been used due to the available solids data.
6.5. Case 5: Mica Case Study.
Reference: BHR Group.
Description: This is an example of an existing mica slurry transportation system which when originally constructed had a total length of 1800m of 80mm ID pipework and a throughput of 5.2t/h of mica solids (density 2650 kg/m3).
It was intended to extend the pipeline by 250m resulting in a new total length of 2050m. The corresponding increase in net elevation change was +66.2m to 80m. The throughput was also to increase to approximately 9.53 t/h.
The new pipe length was divided into 17 sections of known length and elevation change as set out in the Table below.
|
Pipe Section |
Length (m) |
Elevation Change |
|
S1 |
137.5 |
+6.3 |
|
S2 |
87.5 |
+2.5 |
|
S3 |
62.5 |
0 |
|
S4 |
137.5 |
+8.2 |
|
S5 |
225 |
+15.1 |
|
S6 |
75 |
+1.9 |
|
S7 |
100 |
+2.8 |
|
S8 |
50 |
+2.2 |
|
S9 |
100 |
+6.8 |
|
S10 |
50 |
+1.5 |
|
S11 |
62.5 |
+6 |
|
S12 |
112.5 |
+10 |
|
S13 |
100 |
+4.9 |
|
S14 |
50 |
13.8 |
|
S15 |
50 |
0 |
|
S16 |
400 |
0 |
|
S17 |
250 |
0 |
|
Total |
2050 |
+80 |
Using this data, a model was developed in FluidFlow.
FluidFlow Model
Required Information:
- Total System Pressure Differential.
- Ensure pipeline velocity > deposition velocity.
A study had previously been completed on this system by Engineering Consultants using the SRC Two-Layer Model approach. Based on historical test data available and the results of the SRC analysis, a model of the system was developed. Using the Liu Dezhong method, FluidFlow was used to analyse the system and the calculated results correlated with the SRC approach. The system was solved for a known particle distribution on the basis of a slurry concentration of 20% by weight and a total system volumetric flow rate of 41.7 m3/h. Details of the findings are outlined in the table below.
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pipe Velocity (m/s) |
2.31 |
2.3 |
|
Deposition Velocity (m/s) |
1.6 |
1.53 |
|
Total Differential Pressure (bar) |
21.9 |
20.3 |
|
Solids Delivered (t/h) |
9.53 |
9.51 |
Commentary:
The results correlate extremely well, with negligible difference between the two results. The FluidFlow results are a very close match to that of the data for the actual system.
6.6 Case 6: 800M Vertical Pipe - Heterogeneous Slurry.
Reference: Warman Slurry Handbook, 2009, Pg 32.
Description: In an iron-ore mine the ore is ground to 100 µm (0.1mm) in a sub-surface facility and then pumped vertically 800m to the surface. The pipe has a diameter of 0.2m. The concentration by volume is 20% and the specific gravity of the solids is 4.9. Determine the pressure requirement to pump the slurry to the surface at a velocity of 2m/s.
FluidFlow Model
Pipe Data Entry
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure Requirement (MPa) |
14.2 |
14.25 |
Commentary:
The results correlate extremely well, with negligible difference between the two results.
7. Pulp & Paper
7.1. Case 1: Pulp & Paper System (Chemical Pulp).
Reference: ScanPump Brochure, Example 2.4.
Description: A pipeline transports pulp/paper stock with a wt% oven dry concentration of 2.7 %. The pipeline has a length of 72.6 M (approx. 238 ft), an I.D. of 300mm and the pipe absolute roughness is 0.00087mm. The system flow rate is 281 m3/h and the water temperature is 30oC. The pipe also experiences a change in elevation from 0 m to 19 M. The aspect ratio is 60 and the pulp has a freeness of 500 Csf.
Determine the overall pressure loss in the pipeline.
FluidFlow Model
Pipe Data Entry
Result Comparison:
|
Description |
Published Data |
FluidFlow Results |
|
Pressure (m fluid) |
22 |
22.71 |
Commentary:
The results correlate extremely well, with negligible difference between the two results. This system has been solved using the TAPPI approach.