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Leak Rate Determination
AppendixBI361
Appendix B
Leak Rate Determination
Fluid flow through pipelines is a complex and not completely understood problem. It is the subject of continuing research by engineers, physicists, and, more recently, those studying nonlinear dynamic systems, popularly called the science of chaos. In a relative risk assessment, we are less concerned with exact numerical solutions, and more interested in comparative values. In general, fluid flow in pipes is assigned to one of two flow regimes, turbulent or laminar. Some make distinctions between rough turbulent and smooth turbulent, and a region termed the transition zone is also recognized. However, in simplest terms, the flow pattern will be characterized by uniform, parallel velocities of fluid particles--laminar flow---or by turbulent eddies and circular patterns of fluid particle velocities--turbulent flow--or by some pattern that is a combination of the two. The flow pattern is dependent on the fluid average velocity, the fluid kinematic viscosity, the pipe diameter, and the roughness of the inside wall of the pipe. Several formulas that relate these parameters to fluid density and pressure drop offer approximate solutions for each flow regime. These formulas make a distinction between compressible and non-compressible fluids. Liquids such as crude oil, gasoline, and water are considered to be non-compressible, whereas gases such as methane, nitrogen, and oxygen are considered to be compressible. Highly volatile products such as ethylene, propane, and propylene are generally transported as dense gases--they are compressed in the pipeline until their properties resemble those of a liquid, but will immediately return to a gaseous state on release of the pressure. For purposes of a relative risk assessment, any consistent method of flow calculation can be used. Because the primary intent here is not to perform flow calculations but rather to quickly determine relative leak quantities, some simplifying parameters are in order. Original (first two editions of this book) suggestions for calculations of a Leak Impact Factor (Chapter 7) used the following modeling simplifications:
9 Release duration is arbitrarily chosen at 10 minutes for a gas and 60 minutes for a liquid. 9 Complete line rupture (guillotine-type failure) is used.* 9 Operation at MAOP is taken as the initial condition.t 9 Initial conditions are assumed to continue for the entire release duration (except for flashing fluids). 9 Depressurization, flow reductions, etc., which occur during the release scenario, are generally ignored. 9 An arbitrary transition point from liquid to gas is chosen for flashing fluids. 9 Pooling of liquids and vapor generation from those pools is ignored. 9 Temperature effects are ignored in the equations but should be considered in choosing the liquid calculation versus the gas calculation. The evaluator should assume the worst case, for example, a butane release on a cold day versus a hot day. 9 Pressure due to elevation effects is considered to be a part of MAOP. These are oiten conservative and appropriate assumptions for risk modeling. However, using any simplifying parameters must not mask a worst case scenario. The parameters are selected to usually reflect conservative, worst case scenarios. The evaluator must affirm that one or more of the above parameters does not actually reflect a less severe scenario. Again, almost any consistent modeling of a leak quantity will serve the purpose of a relative risk assessment. Consistency is absolutely critical, however. One approach that is currently in use involves the above parameters and model releases as follows: 9 Gas--the quantity of gas released from a full-bore line ruptured at MAOP (or normal operating pressure) for 10 minutes. "Reasoning behind selection of this parameter is provided in Chapter 7. tAs an alternative, the evaluator can use a pressure profile to determine maximum expected pressure.
362 Leak Rate Determination
9 Liquid--the quantity of liquid released from a full-bore line rupture at MAOP (for normal operating pressure) for 1 hour (60 minutes). An alternative approach is to model the spill volume as the maximum pumped flowrate for a fixed time period (perhaps based on estimated reaction times) plus the volume that would be drained to the spill location. 9 Flashing fluidmthe quantity of liquid released from a fullbore line rupture at MAOP (or normal operating pressure) for 3 minutes plus the quantity of gas released from a fullbore line rupture at the product's vapor pressure for 7 minutes (see Figure B. 1).
upstream condition. Sonic velocity is a limiting factor for gas flow through an orifice.
Liquid flow For incompressible fluids, the equation of flow through an orifice is essentially the same with the exception of the expansion factor, Y, which is not needed for the case of incompressible fluids [23]" /
q = CA [ V
(2g) 144AP P
where
Gas flow For compressible fluids, a calculation for flow through an orifice can be used to approximate the flow rate escaping the pipeline [23]: /
q = YCA .[
(2g) 144AP
V
P
where Y A C g AP p q
= = = = = = =
expansion factor (usually between 0.65 and 0.95) cross-sectional area ofthe pipe (ft 2) flow coefficient (usually between 0.9 and 1.2) acceleration of gravity (32.2 ft/sec per second) change in pressure across the orifice (psi) weight density of fluid (lb/ft 3) flow rate (ft3/sec).
In the case of a discharge of the fluid to atmosphere (or other low pressure environment), Y can be taken at its minimum value, and the weight density of the fluid should be taken at the
MAOP (or normal operating pressure)
Mass of liquid
Vapor pressure
Mass of gas
0L U') U) t9 t._
Gas
EL
phase release
0 min
3 min Time
10 min D,
Spill Quantity = (Mass of Liquid) + (Mass of Gas) Figure B.1 Spillquantitymodel for a flashing fluid.
A C g AP p q
= = = = = =
cross-sectional area ofthe pipe (ft 2) flow coefficient (usually between 0.9 and 1.2) acceleration of gravity (32.2 ft/sec per second) change in pressure across the orifice (psi) weight density of fluid (lb/ft 3) flow rate (ft3/sec).
Alternately, other common liquid flow equations such as the Darcy equation can be used to calculate this flow. A consistent approach is the important thing. Note that continued pumping rate and drain volumes are often the determining factor of a liquid pipeline spill. These calculations might be more appropriate than the orifice flow calculation for liquid pipelines. Drain calculations may take into account siphoning possibilities, but that might also be an unnecessary modeling complication. Crane Valve [23] should be consulted for a complete discussion of these flow equations.
Flashing fluids/highly volatile liquids Fluids that flash, that is, that transform from a liquid to a gaseous state on release from the pipeline, pose a complicated problem for leak rate calculation. Initially, droplets of liquid, gas, and aerosol mists will be generated in some combination. These may form liquid pools that continue to generate vapors. The vapor generation is dependent on temperature, soil heat transfer, and atmospheric conditions. It is a nonlinear problem that is not readily solvable. Eventually, if the conditions are right, the liquid will all flash or vaporize and the flow will be purely gaseous. To simplify this problem, an arbitrary scenario is chosen to simulate this complex flow. Three minutes of liquid flow at MAOP is added to 7 minutes of gas flow at the product's vapor pressure to arrive at the total release quantity after 10 minutes. This conservatively simulates a situation in which, on pipeline rupture, pure liquid is released until the nearby pipeline contents are depressured from the rupture pressure to the product's vapor pressure. Three minutes at the higher pressure--the initial pressure (MAOP)--simulates this. Then, when the nearby pipe contents have reached the product's vapor pressure, any liquid remaining in the line will vaporize. This vapor generation is simulated by 7 minutes of gas flow at the vapor pressure of the pipeline contents. Figure B. 1 illustrates this concept. This is, of course, a gross oversimplification of the actual process. For this application however, the scenario, if applied consistently, should provide results to make adequate distinctions in leak rates between pipelines of different products, sizes, and pressures.
Appendix B
Leak Rate Determination
Fluid flow through pipelines is a complex and not completely understood problem. It is the subject of continuing research by engineers, physicists, and, more recently, those studying nonlinear dynamic systems, popularly called the science of chaos. In a relative risk assessment, we are less concerned with exact numerical solutions, and more interested in comparative values. In general, fluid flow in pipes is assigned to one of two flow regimes, turbulent or laminar. Some make distinctions between rough turbulent and smooth turbulent, and a region termed the transition zone is also recognized. However, in simplest terms, the flow pattern will be characterized by uniform, parallel velocities of fluid particles--laminar flow---or by turbulent eddies and circular patterns of fluid particle velocities--turbulent flow--or by some pattern that is a combination of the two. The flow pattern is dependent on the fluid average velocity, the fluid kinematic viscosity, the pipe diameter, and the roughness of the inside wall of the pipe. Several formulas that relate these parameters to fluid density and pressure drop offer approximate solutions for each flow regime. These formulas make a distinction between compressible and non-compressible fluids. Liquids such as crude oil, gasoline, and water are considered to be non-compressible, whereas gases such as methane, nitrogen, and oxygen are considered to be compressible. Highly volatile products such as ethylene, propane, and propylene are generally transported as dense gases--they are compressed in the pipeline until their properties resemble those of a liquid, but will immediately return to a gaseous state on release of the pressure. For purposes of a relative risk assessment, any consistent method of flow calculation can be used. Because the primary intent here is not to perform flow calculations but rather to quickly determine relative leak quantities, some simplifying parameters are in order. Original (first two editions of this book) suggestions for calculations of a Leak Impact Factor (Chapter 7) used the following modeling simplifications:
9 Release duration is arbitrarily chosen at 10 minutes for a gas and 60 minutes for a liquid. 9 Complete line rupture (guillotine-type failure) is used.* 9 Operation at MAOP is taken as the initial condition.t 9 Initial conditions are assumed to continue for the entire release duration (except for flashing fluids). 9 Depressurization, flow reductions, etc., which occur during the release scenario, are generally ignored. 9 An arbitrary transition point from liquid to gas is chosen for flashing fluids. 9 Pooling of liquids and vapor generation from those pools is ignored. 9 Temperature effects are ignored in the equations but should be considered in choosing the liquid calculation versus the gas calculation. The evaluator should assume the worst case, for example, a butane release on a cold day versus a hot day. 9 Pressure due to elevation effects is considered to be a part of MAOP. These are oiten conservative and appropriate assumptions for risk modeling. However, using any simplifying parameters must not mask a worst case scenario. The parameters are selected to usually reflect conservative, worst case scenarios. The evaluator must affirm that one or more of the above parameters does not actually reflect a less severe scenario. Again, almost any consistent modeling of a leak quantity will serve the purpose of a relative risk assessment. Consistency is absolutely critical, however. One approach that is currently in use involves the above parameters and model releases as follows: 9 Gas--the quantity of gas released from a full-bore line ruptured at MAOP (or normal operating pressure) for 10 minutes. "Reasoning behind selection of this parameter is provided in Chapter 7. tAs an alternative, the evaluator can use a pressure profile to determine maximum expected pressure.
362 Leak Rate Determination
9 Liquid--the quantity of liquid released from a full-bore line rupture at MAOP (for normal operating pressure) for 1 hour (60 minutes). An alternative approach is to model the spill volume as the maximum pumped flowrate for a fixed time period (perhaps based on estimated reaction times) plus the volume that would be drained to the spill location. 9 Flashing fluidmthe quantity of liquid released from a fullbore line rupture at MAOP (or normal operating pressure) for 3 minutes plus the quantity of gas released from a fullbore line rupture at the product's vapor pressure for 7 minutes (see Figure B. 1).
upstream condition. Sonic velocity is a limiting factor for gas flow through an orifice.
Liquid flow For incompressible fluids, the equation of flow through an orifice is essentially the same with the exception of the expansion factor, Y, which is not needed for the case of incompressible fluids [23]" /
q = CA [ V
(2g) 144AP P
where
Gas flow For compressible fluids, a calculation for flow through an orifice can be used to approximate the flow rate escaping the pipeline [23]: /
q = YCA .[
(2g) 144AP
V
P
where Y A C g AP p q
= = = = = = =
expansion factor (usually between 0.65 and 0.95) cross-sectional area ofthe pipe (ft 2) flow coefficient (usually between 0.9 and 1.2) acceleration of gravity (32.2 ft/sec per second) change in pressure across the orifice (psi) weight density of fluid (lb/ft 3) flow rate (ft3/sec).
In the case of a discharge of the fluid to atmosphere (or other low pressure environment), Y can be taken at its minimum value, and the weight density of the fluid should be taken at the
MAOP (or normal operating pressure)
Mass of liquid
Vapor pressure
Mass of gas
0L U') U) t9 t._
Gas
EL
phase release
0 min
3 min Time
10 min D,
Spill Quantity = (Mass of Liquid) + (Mass of Gas) Figure B.1 Spillquantitymodel for a flashing fluid.
A C g AP p q
= = = = = =
cross-sectional area ofthe pipe (ft 2) flow coefficient (usually between 0.9 and 1.2) acceleration of gravity (32.2 ft/sec per second) change in pressure across the orifice (psi) weight density of fluid (lb/ft 3) flow rate (ft3/sec).
Alternately, other common liquid flow equations such as the Darcy equation can be used to calculate this flow. A consistent approach is the important thing. Note that continued pumping rate and drain volumes are often the determining factor of a liquid pipeline spill. These calculations might be more appropriate than the orifice flow calculation for liquid pipelines. Drain calculations may take into account siphoning possibilities, but that might also be an unnecessary modeling complication. Crane Valve [23] should be consulted for a complete discussion of these flow equations.
Flashing fluids/highly volatile liquids Fluids that flash, that is, that transform from a liquid to a gaseous state on release from the pipeline, pose a complicated problem for leak rate calculation. Initially, droplets of liquid, gas, and aerosol mists will be generated in some combination. These may form liquid pools that continue to generate vapors. The vapor generation is dependent on temperature, soil heat transfer, and atmospheric conditions. It is a nonlinear problem that is not readily solvable. Eventually, if the conditions are right, the liquid will all flash or vaporize and the flow will be purely gaseous. To simplify this problem, an arbitrary scenario is chosen to simulate this complex flow. Three minutes of liquid flow at MAOP is added to 7 minutes of gas flow at the product's vapor pressure to arrive at the total release quantity after 10 minutes. This conservatively simulates a situation in which, on pipeline rupture, pure liquid is released until the nearby pipeline contents are depressured from the rupture pressure to the product's vapor pressure. Three minutes at the higher pressure--the initial pressure (MAOP)--simulates this. Then, when the nearby pipe contents have reached the product's vapor pressure, any liquid remaining in the line will vaporize. This vapor generation is simulated by 7 minutes of gas flow at the vapor pressure of the pipeline contents. Figure B. 1 illustrates this concept. This is, of course, a gross oversimplification of the actual process. For this application however, the scenario, if applied consistently, should provide results to make adequate distinctions in leak rates between pipelines of different products, sizes, and pressures.