CHAPTER 4: GAS FLOW CALCULATIONS AND SIZING OF PIPE TABLE OF CONTENTS
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Introduction................................................................................................................................................ 1
Gas Flow Fundamentals............................................................................................................................ 1
Types of Gas Flow ................................................................................................................................ 1
Reynolds Number ................................................................................................................................. 2
General Flow Behavior.......................................................................................................................... 3
Steel Pipe at Pressures Over 30 Psig................................................................................................... 3
Other Fully Turbulent Equations ........................................................................................................... 5
Flow Equation Parameters.................................................................................................................... 6
Flow Calculations....................................................................................................................................... 7
Resistance Factors ............................................................................................................................... 7
Calculating Upstream Pressure .......................................................................................................... 12
Sizing Service Lines ................................................................................................................................ 14
Equivalent Length ............................................................................................................................... 14
LIST OF TABLES
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Table 4-1: General Flow Behavior ............................................................................................................ 3
Table 4-2: Partially Turbulent Flow Equations.......................................................................................... 4
Table 4-3: Fully Turbulent Flow Equation................................................................................................. 4
Table 4-4: Partially Turbulent and Fully Turbulent Equations................................................................... 6
Table 4-5: Resistance Factors and Flow Equations ................................................................................. 8
Table 4-6: Values of Critical Reynolds Numbers for Steel Pipe Average Wall Roughness...................... 9
Table 4-7: Values of Critical Reynolds Numbers for Steel Pipe, Pipe Walls Rougher than Normal ......... 9
Table 4-8: Resistance Factors................................................................................................................ 11
Table 4-9: Equivalent Length Data ......................................................................................................... 15
Table 4-10: Equivalent Lengths for Low-Pressure Service Pipe ............................................................. 15
LIST OF FIGURES
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Figure 4-1: Methane-Fueled Laminar Flame ............................................................................................ 1
Figure 4-2: Turbulent Flow........................................................................................................................ 2
Figure 4-3: Partially Turbulent Flow.......................................................................................................... 2
Figure 4-4: Service Line Installation ....................................................................................................... 14
Figure 4-5: Attachment to MP Steel Main............................................................................................... 15
Figure 4-6: Swing Joint Connection to CI LP.......................................................................................... 15
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CHAPTER 4: GAS FLOW CALCULATIONS AND SIZING OF PIPE
Introduction After gas loads are properly estimated (as presented in Chapter 3), the next step is to perform flow calculations to determine if the existing pipe network and facilities in an area will be able to supply the load and maintain adequate pressure during peak demand. If it is determined that existing facilities are inadequate, new lines must be properly sized to maintain adequate pressure at design “peak” loads. This chapter addresses basic flow-calculation procedures and their use in pipe sizing.
Gas Flow Fundamentals Gas flow in distribution piping occurs as the result of a difference between upstream and downstream pressures. The pressure of gas flowing through a pipe of uniform diameter gradually decreases in the direction of flow. The magnitude of the pressure drop depends on several flow variables:
• Flow rate
• Pipe diameter
• Inside pipe wall roughness (friction)
• Pressure
• Gas properties
Flow variables can be calculated by substituting known data and gas properties into an appropriate equation. To select the proper flow equation, you must first determine the type of flow.
Types of Gas Flow Osborne Reynolds, an early investigator of fluid mechanics, studied flow patterns in pipe and discovered that the type of flow depends on variables that are similar to those that affect pressure drop. These include flow rate, pipe diameter, viscosity (vs. friction) and density (vs. pressure). Reynolds demonstrated that two basic types of flow occur in a pipe: laminar and turbulent flow. Laminar Flow: In laminar flow, gas will travel in a straight line parallel to the pipe walls. This will occur if inside pipe walls are perfectly smooth and offer no resistance to flow. Flow that resembles this pattern will occur in plastic pipe at very low flow rates.
Figure 4-1: Methane-Fueled Laminar Flame Turbulent Flow: In turbulent flow, gas will travel in a convoluted pattern. Turbulent flow will occur at high velocities—such as peak flow periodsand in piping with rough inside wall surfaces or debris. Examples of pipe with turbulent flow include older steel pipe and cast iron.
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Figure 4-2: Turbulent Flow
Reynolds Number The combination of the four variables identified by Osborne Reynolds—flow rate, pipe diameter, viscosity, and density—yield a dimensionless parameter known as the Reynolds number. Mathematically, the Reynolds number is expressed by the following equation: Reynolds Number Equation Re = DVρ/μ
• Re = Reynolds number
• D = diameter
• V = velocity
• ρ = density
• μ = viscosity
Analysis of the Reynolds number shows that it is the ratio of the inertia forces to the viscous forces involved in flow. Depending on the value of the Reynolds number, either the viscous forces will predominateyielding laminar flowor the inertia forces will predominateyielding turbulent flow. Further studies of flow rates and Reynolds numbers established that turbulent flow will occur at design load conditions (high flow rates). However, the transition from laminar to turbulent flow is not abrupt and complete. As a result, two types of turbulent flow have been definedpartially turbulent flow and fully turbulent flow.
Figure 4-3: Partially Turbulent Flow As stated previously, you must first determine the type of flow in order to select the proper flow equation. The flow equations are based on whether you have partially turbulent or fully turbulent flow. The Reynolds number provides a method to determine if flow is laminar, partially turbulent, or fully turbulent.
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General Flow Behavior Flow studies and information on pipe wall roughness, Reynolds numbers, and empirical measurements have determined the general flow behavior for a limited range of flow conditions as follows:
Table 4-1: General Flow Behavior
Pipe Conditions
Flow Behavior
Plastic pipe
Partially turbulent flow
Clean, low pressure cast iron pipe
Partially turbulent flow
Clean steel pipe at pressures up to 30 psig (207 kPa)
Partially turbulent flow with average wall roughness no greater than 0.7 mil (0.018 mm)
Steel pipe at pressures over 30 psig (207 kPa)
Partial or fully turbulent flow (see following section)
Steel Pipe at Pressures Over 30 psig A practical method to determine the type of turbulent flow for steel pipe over 30 psig is to use the “critical” Reynolds number. At Reynolds numbers below the critical value, partially turbulent flow will occur. At Reynolds numbers greater than the critical value, fully turbulent flow will occur. The critical Reynolds number is determined by two methods, depending on whether you are solving for pressure or diameter or flow-rate.
1) Solving for Pressure
When solving for upstream or downstream pressure, the subsequent steps are followed: 1. Calculate the Reynolds number for the given conditions. 2. Compare the Reynolds number to the critical Reynolds number for the given conditions. 3. If the calculated Reynolds number is less than the critical Reynolds number, select a partially turbulent flow equation that meets the given conditions. 4. If the calculated Reynolds number is greater than the critical Reynolds number, use the fully turbulent equation. 5. Solve the appropriate flow equation for upstream or downstream pressure.
2) Solving for Diameter or Flow Rate
When solving for pipe diameter or flow rate, the Reynolds number cannot first be calculated (as above), because the pipe diameter or flow rate is needed to solve for the Reynolds number. As a result, the following steps are used:
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1. Initially assume you have partially turbulent flow. Partially turbulent flow is the most prevalent type in distribution systems. 2. Select a partially turbulent flow equation that meets the given conditions. This will normally be the IGT Distribution equation. 3. Calculate the pipe diameter or flow rate using the selected equation. 4. Solve for the Reynolds number using the resulting value from step 3. If the calculated Reynolds number is less than the critical Reynolds number, the solution is valid. 5. If the calculated value is greater than the critical Reynolds number, the first solution is not valid and the calculation must be performed using the fully turbulent flow equation. Flow Equations After determining whether you have partially or fully turbulent flow, an equation is selected based on pipe diameter and pressure. Note there is only one equation that is primarily used for fully turbulent pipe flow.
Table 4-2: Partially Turbulent Flow Equations
Table 4-3: Fully Turbulent Flow Equation Flow Equation Limitations Standard flow equations are not applicable for use in sizing smaller sections of pipe. Those sections are listed here:
• Short by-passes
• Relief vents
CHAPTER 4 GAS FLOW CALCULATIONS AND SIZING OF PIPE 4-5
• Regulator station outlets
• Meter and regulator piping.
Welds, fittings, and debris generate additional turbulence. As a result, some companies apply factors to the equations in order to represent flow behavior more closely. Factors are also used to correct for significant elevation changes.
Other Fully Turbulent Equations There are other equations occasionally used for fully turbulent pipe flow because of simplicity. The high-pressure Spitzglass and Weymouth formulas are used for rough estimates but are not recommended. Their limitations are listed below: Spitzglass High-Pressure Equation The Spitzglass High-pressure Equation is based on a transmission factor expression that represents fully turbulent flow behavior, but it is almost never used for that purpose. It is used primarily to make flow calculations in cast iron low-pressure distribution systems where partially turbulent flow predominates. Its transmission factor expression was developed in 1912 from flow tests on large-diameter cast iron pipes operated at inches w.c. pressure and at flow conditions that probably resulted in partially turbulent flow. Weymouth Equation The Weymouth Equation is used extensively to represent fully turbulent flow behavior. However, it is necessary to use an empirically determined correction factor to get a good simulation. The form of the factor normally used is an efficiency factor, E, that is applied as a multiplier to the flow rate. The uncorrected Weymouth Equation predicts a lower flow rate for specified flow conditions than is actually experienced. Its primary application is for flow calculations for large-diameter, high-pressure pipelines on which field flow tests can be readily performed to evaluate the efficiency factor and monitor line performance. Because efficiency factors cannot normally be developed for sections of distribution pipe, use of this equation for distribution flow calculations is not recommended. All of the partially turbulent and fully turbulent equations are listed in Table 4-4. The terms (or flow parameters) used in the equations are identified below the table.
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Table 4-4: Partially Turbulent and Fully Turbulent Equations
Flow Equation Parameters Parameters listed in the gas flow equations have been grouped into the following categories:
• Constants: Base pressure = Pb, the value of which is usually taken to be 14.73 psia (101.56 kPa) Base temperature = Tb, the value of which is usually taken to be 5200R (288.89K)
• Gas Properties: Specific gravity = G, Viscosity = p, Average Compressibility Factor = Zavg
The values of the gas properties depend primarily on its composition and normally do not vary from one section of pipe to the next in a gas distribution system. At pressures up to 100 psig (689 kPa), the value of Zavg can be taken as 1.0.
• Gas Pressures: In taking pressure measurements, confusion arises because the zero point on most pressure gauges represents atmospheric pressure rather than zero absolute pressure. This makes it necessary to specify the kind of pressure being measured under given conditions.
Gauge pressure is the pressure actually shown on the dial of a gauge that is registering pressure relative to atmospheric pressure. An ordinary pressure gauge reading of zero does not mean there is no pressure in the absolute sense; rather, it means there is no pressure in excess of atmospheric pressure. Atmospheric Pressure is the pressure exerted by the weight of the atmosphere. At sea level, the atmosphere exerts a pressure that is equal to about 14.7 psia. Atmospheric pressure at sea level is 14.7 pounds per square inch absolute (psia). It is zero on an ordinary pressure gauge.
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CHAPTER 4 GAS FLOW CALCULATIONS AND SIZING OF PIPE 4-7
Absolute Pressure is atmospheric pressure plus gauge pressure. For example, a gauge pressure of 300 pounds per square inch gauge (psig) equals an absolute pressure of 314.7 psia (300+ 14.7). Sometimes psig is used to indicate gauge pressure and other times psi (only) is written. By common convention, gauge pressure is always assumed when pressure is given in pounds per square inch, pounds per square foot, or similar units. The g, for gauge, is added only when there is some possibility of confusion. Absolute pressure, on the other hand, is always expressed as pounds per square inch absolute (psia) and pounds per square foot absolute (psia). It is necessary to establish clearly just what kind of pressure we are talking about, unless this is very clear from the nature of the discussion.
• Gas Temperatures: Absolute temperature is the temperature relative to absolute zero in Kelvin or Rankin units. (ºR= temperature in ºFahrenheit + 460 º; º Kelvin = º Celsius + 273 º) Absolute temperature of the flowing gas = Tavg, (or Tf). The flowing gas temperature is approximated as the ground temperature expressed in units of absolute temperature and varies with geographic location and season.
• Pipe Properties: Effective wall roughness = k , Friction factors represent partially turbulent and fully turbulent flows in the flow equations and are known by other names such as transmission factors, Darcy-Weisbach factors, smooth and rough pipe expressions, and other terms. Note that friction factors are not a constant parameter, but are proportional to flow.
• Flow Variables: Pressure drop in low-pressure systems = P, or the difference in the squares of the upstream and downstream absolute pressures, (P12 -P22 ). Absolute pressure, psia = gauge pressure, psig + atmospheric pressure, patm
Gas Flow Rate = Qb - the units for Qb are “standard cubic feet” for the flow equations and MCFH “thousand cubic feet” in the Reynolds formula. Pipe Diameter = D, which is inside diameter. Pipe length = L. These flow variables change from one flow problem to the next. In most flow calculations, the values of all but one of the flow variables are known and the objective of the calculation is to determine the value of the unknown. Current flow formulas are quite complex because of the change in turbulence under different flow conditions. However, prior to their development, errors of more than 30% were found between calculated and measured data on new piping. Much greater error was found on corroded or debris filled lines.
Flow Calculations Engineers have developed a method to simplify the flow equations by combining various parameters into a “resistance factor” (R).
Resistance Factors For manual flow calculations, all the constants, the gas properties, the flowing gas temperature, and the diameter term from the flow equations can be combined to obtain a convenient quantity called the pipe section unit length resistance factor (R). Partially turbulent and fully turbulent flows are represented by different resistance factors in flow equations.
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All flow equations can then be expressed in the simplified form: P2 = RLQbn = KQbn where: P = pressure drop R = resistance factor per unit length of pipe, K/L L = pipe length Qb = flow rate n = flow rate exponent whose value ranges from 1.74 to 2.0, depending on the flow equation used K = pipe section friction factor The resistance-factor expressions (R) and value of the exponent (n) are summarized in the following table for the common flow equations.
Table 4-5: Resistance Factors and Flow Equations The next tables list critical Reynolds numbers and dimensions for steel pipe. These are the numbers used in flow equations when solving for upstream pressure, downstream pressure, pipe diameter, or flow rate.
CHAPTER 4 GAS FLOW CALCULATIONS AND SIZING OF PIPE 4-9
Table 4-6: Values of Critical Reynolds Numbers for Steel Pipe Average Wall Roughness
Nominal Pipe Diameter (inches)
Schedule Number (the nominal designation for pipe wall thickness)
Actual Inside Diameter (inches)
Critical Reynolds Numbers (Re thousands)
1
40
1.049
117
1 ¼
40
1.380
159
1 ½
40
1.610
189
2
40
2.067
249
4
40
4.026
520
6
40
6.065
816
8
40
7.981
1,100
10
20
10.250
1,450
12
20
12.250
1,760
16
20
15.376
2,250
20
20
19.250
2,880
24
20
23.250
3530
30
20
29.000
4,490
(k = 0.7 mil) and (k = effective roughness of the pipe wall; mill = 10-3 inches)
Table 4-7: Values of Critical Reynolds Numbers for Steel Pipe, Pipe Walls Rougher than Normal
Nominal Pipe Diameter (inches)
Schedule Number (the nominal designation for pipe wall thickness)
Actual Inside Diameter (inches)
Critical Reynolds Numbers (Re thousands)
1
40
1.049
36.1
1 ¼
40
1.380
49.1
1 ½
40
1.610
58.5
2
40
2.067
77.4
4
40
4.026
163
6
40
6.065
257
8
40
7.981
348
10
20
10.028
447
12
20
12.250
557
16
20
15.376
708
20
20
19.250
914
24
20
23.250
1127
30
20
29.000
1430
(k = 2.0 mil) (k = effective roughness of the pipe wall; mill = 10 −3 inches) The following examples illustrate the principal application of flow equations and the resistance factor (R) in pipe flow calculations.
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Example Problem 1: Computing Downstream Pressure Given Information: Gas is fed into a mile-long (1.61 kilometer) section of 4-inch (102 millimeter) schedule-40 steel pipe. The upstream pressure is 20 psig (138 kPa) and flow rate is 30 MCFh. The atmospheric pressure, base conditions, flowing gas temperature, and gas properties are as follows:
• Pb = 14.73 psia
• Atmospheric Pressure = 14.7 psia
• Tb = 520º Rankin
• Tf = 490º Rankin (actual temperature of gas)
• G = 0.60
• μ = 7.23 X 10-6Ibm/fts
Step 1: Determine if you have partially turbulent or fully turbulent flow. Partially turbulent flow is assumed because you have a new steel pipe operating at a pressure less than 30 psig. This is based on the general flow behavior chart, Table 4-1. Step 2: Calculate the Reynolds number. To select an appropriate flow equation, the Reynolds number for the flow conditions must be computed for the given conditions. The formula for Reynolds number (Re) expressed in terms of flow equation variables is as follows: Re = (0.011459) QbGPb / (uDTb) Re = (0.011459 X 0.6 X 14.73) Qb / (7.23 x 10-6) (520) D 4.026 is the inside diameter for 4-inch schedule-40 steel pipe. This number is from the table of critical Reynolds numbers for steel. Re = (.011459 X 30,000 X .6 X 14.73) / (7.23 X 4.026 X 10-6 X 520) = 200,700. Step 3: Compare the computed Reynolds number from Step 2 to the critical Reynolds number for 4-inch (102-mm) schedule-40 steel pipe. Locate the Critical Reynolds number from the table of critical Reynolds numbers for 4-inch pipe of average wall roughness, 0.7 mil. The critical number is 520,000. 200,700 < 520,000 Because the calculated Reynolds number is less than the critical Reynolds number, a partially turbulent flow equation should be used. Step 4: Select a partially turbulent equation (from Table 4-2, repeated below) and resistance factor that fits the given parameters.
CHAPTER 4 GAS FLOW CALCULATIONS AND SIZING OF PIPE 4-11
The
