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Section 5 Consequence Analysis 5.1 Dispersion Analysis

Section 5 Consequence Analysis 5.1 Dispersion Analysis. Process Control & Safety Group Institute of Hydrogen Economy Universiti Teknologi Malaysia Dr. Arshad Ahmad Email: arshad@cheme.utm.my. www.utm.my. innovative ● entrepreneurial ● global. Accident Happens.

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Section 5 Consequence Analysis 5.1 Dispersion Analysis

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  1. Section 5Consequence Analysis5.1 Dispersion Analysis Process Control & Safety Group Institute of Hydrogen Economy Universiti Teknologi Malaysia Dr. Arshad Ahmad Email: arshad@cheme.utm.my www.utm.my innovative ● entrepreneurial ● global

  2. Accident Happens Spills of materials can lead to disaster toxic exposure Fire explosion Materials are released from holes, cracks in various plant components Tanks, pipes, pumps Flanges, valves,

  3. Source Model Arshad Ahmad Professor of Process Control & Safety Director, Institute of Hydrogen Economy, UTM

  4. Various types of limited aperture releases.

  5. Release Mechanism • Wide Aperture • Release of substantial amount in short time • example: Overpressure of tank and explosion • Limited Aperture • Release from cracks, leaks etc • Relief system is designed to prevent over-pressure

  6. Source Models Source models represent the material release process Provide useful information for determining the consequences of an accident rate of material release, the total quantity released, and the physical state of the material. valuable for evaluating new process designs, process improvements and the safety of existing processes.

  7. Release of Gasses Gasses/vapours Disperse to atmosphere Gas / Vapour Leak Gas / Vapour

  8. Release of Liquids Gasses/vapours Disperse to atmosphere Vapour or Two Phase Liquid Vapour Liquid • Liquid flashes into vapour • Liquid collected as in a pool

  9. Basic Models Flow of liquids through a hole Flow of liquids through a hole in a tank Flow of liquids through pipes Flow of vapor through holes Flow of vapor through pipes Flashing liquids Liquid pool evaporation or boiling

  10. Mechanical Energy Balance General mechanical energy balance Equation (1) • P is the pressure (force/area), • r is the fluid density (mass/volume) • ū is the average instantaneous velocity of the fluid (length/time) • gc is the gravitational constant (length mass/force time²), • a is the unitless velocity profile correction factor - (0.5 for laminar flow, 1.0 for plug flow, >1.0 for turbulent flow) • g is the acceleration due to gravity (length/time²) • z is the height above datum (length) • F is the net frictional loss term (length force/mass) • Wsis the shaft work (force length) • m is the mass flow rate (mass/time)

  11. Mechanical Energy Balance Incompressible Fluid Density is constant No elevation difference (Dz = 0) No shaft work, Ws = 0 Negligible velocity change (small aperture), Du = 0 Typical Simplifications

  12. 1. Flow of Liquid Through Holes External Surrounding P = 1 atm Uave, 2 = Uav A= leak area Liquid pressurized within process units P=Pg Uave= 0 Dz=0 Ws=0 r = liquid density (2) Liquid escaping through a hole in a process unit. The energy of the liquid due to its pressure in the vessel is converted to kinetic energy with some frictional flow losses in the hole.

  13. Discharge Coefficients The following guidelines are suggested to determine discharge coefficients For sharp-edged orifices and for Reynolds number greater than 30,000, Co approaches the value 0.61. For these conditions, the exit velocity of the fluid is independent of the size of the hole. For a well-rounded nozzle the discharge coefficient approaches unity. For short sections of pipe attached to a vessel (with a length-diameter ratio not less than 3), the discharge coefficient is approximately 0.81. For cases where the discharge coefficient is unknown or uncertain, use a value of 1.0 to maximize the computed flows.

  14. 2. Flow of Liquid Through a Hole in a Tank A hole develops at a height hL below the fluid level. The flow of liquid through this hole is represented by the mechanical energy balance assumptions: fluid is incompressible, he shaft work, Ws is zero and the velocity of the fluid in the tank is zero. The mass discharge rate at any time t. The time for the vessel to empty to the level of the leak, te, is

  15. 3. Flow of Liquid Through Pipes • A pressure gradient across the pipe is the driving force • Frictional forces between the liquid and the wall of the pipe converts kinetic energy into thermal energy. This results in a decrease in the liquid velocity and a decrease in the liquid pressure.

  16. Summation of Friction Elements The friction term, F, is the sum of all of the frictional elements in the piping system. For a straight pipe, without valves or fitting, F is given by (12) where ƒ is the Fanning friction factor (no units) L is the length of the pipe d is the diameter of the pipe (length)

  17. Fanning Friction Factor The Fanning friction factor, ƒ, is a function of the Reynolds number, Re, and the roughness of the pipe, e. For laminar flow, the Fanning friction factor is given by For turbulent flow, the data shown in Figure 6 are represented by the Colebrook equation Refer to Figure 6 and roughness in Table 1

  18. Roughness Table 1 Roughness factor, e, for clean pipes.

  19. Fanning Friction Factor Figure 6 Plot of Fanning friction factor, f, versus Reynolds number

  20. Figure 7 Plot of 1/ ƒ, versus Re  ƒ. This form is convenient for certain types of problems. (see Example 2.)

  21. Fittings, elbows etc For piping systems composed of fittings, elbows, valves, and other assorted hardware, the pipe length is adjusted to compensate for the additional friction losses due to these fixtures. The equivalent pipe length is defined as The summation of all of the valves, unions, elbows, and so on, are included in the computation of overall piping equivalent length (see Table 2))

  22. Table 2 Equivalent pipe lengths for various pipe fittings (Turbulent flow only).

  23. Table 2 Equivalent pipe lengths for various pipe fittings (Turbulent flow only)- cont’d

  24. 4. Flow of Vapour Through Holes • For flowing liquids the kinetic energy changes are frequently negligible and the physical properties (particularly the density are constant. • For flowing gases and vapor these assumptions are only valid for small pressure changes (P1/P2 < 2)and low velocities ( 0.3 × speed of sound in gas). • Gas and vapor discharges are classified into throttling and free expansion releases. • For throttling releases, the gas issues through a small crack with large frictional losses; very little of energy inherent with the gas pressure is converted to kinetic energy. • For free expansion releases, most of the pressure energy is converted to kinetic energy; the assumption of isentropic behavior is usually valid. • Source models for throttling releases require detailed information on the physical structure of the leak; they will not be considered here. Free expansion release source models require only the diameter of the leak.

  25. A free expansion leak is shown in Figure 9. The mechanical energy balance, Equation 1, describes the flow of compressible gases and vapors. Assuming negligible potential energy changes and no shaft work results in a reduced form of the mechanical energy balance describing compressible flow through holes. A discharge coefficient, C1, is defined in a similar fashion to the coefficient defined in the first section. Equation 32 is combined with Equation 31 and integrated between any two convenient points. An initial point (denoted by subscript o) is selected where the velocity is zero and the pressure is Po. The integration is carried to any arbitrary final point (denoted without a subscript). The result is (33)

  26. Figure 9 A free expansion gas leak. The gas expands isentropically through the hole. The gas properties (P, T) and velocity change during the expansion

  27. Flow of Vapour Through Holes The resulting equation is: The maximum flowrate is at the choke, Here:

  28. 5. Flow of Vapour Through Pipes Vapor flow through pipes is modeled using two special cases : adiabatic or isothermal behavior. The adiabatic case corresponds to rapid vapor flow through an insulated pipe. The isothermal case corresponds to flow through an uninsulated pipe maintained at a constant temperature; an underwater pipeline is an excellent example. Real vapor flows behave somewhere between the adiabatic and isothermal cases.

  29. For both the isothermal and adiabatic cases it is convenient to define a Mach number as the ratio of the gas velocity to the velocity of sound in the gas at the prevailing conditions. (41) where a is the velocity of sound. The velocity of sound is determined using the thermodynamic relationship. (42) which, for an ideal gas, is equivalent to (43) which demonstrates that, for ideal gases the sonic velocity is a function of temperature only. For air at 20°C the velocity of sound is 344 m/s (1129 ft/s)

  30. Adiabatic Flows An adiabatic pipe containing a flowing vapor is shown in Figure 11. For this particular case the outlet velocity is less than the sonic velocity. The flow is driven by a pressure gradient across the pipe. This expansion leads to an increase in velocity and an increase in the kinetic energy of the gas. The kinetic energy is extracted from the thermal energy of the gas; a decrease in temperature occurs. However, frictional forces are present between the gas and the pipe wall. These frictional forces increase the temperature of the gas. Depending on the magnitude of the kinetic and frictional energy terms either an increase or decrease in the gas temperature is possible.

  31. Figure 11 Adiabatic, non-choked flow of gas through a pipe. The gas temperature might increase or decrease, depending on the magnitude of the frictional losses

  32. The mechanical energy balance, Equation 1, also applies to adiabatic flows. For this case it is more conveniently written in the form (44) the following assumptions are valid for this case : is valid for gases, and From Equation 23, assuming constant f, and

  33. Since no mechanical linkages are present. An important part of the frictional loss term is the assumption of a constant Fanning friction factor, f, across the length of the pipe. This assumption is only valid at high Reynolds number. A total energy balance is useful for describing the temperature changes within the flowing gas. For this open, steady flow process it is given by (45) Where h is the enthalpy of the gas and q is the heat. The following assumptions are invoked. for an ideal gas, is valid for gases, since the pipe is adiabatic, since no mechanical linkages are present.

  34. The above assumptions are applied to Equations 45 and 44. The equations are combined, integrated (between the initial point denoted subscript o and any arbitrary final point), and manipulated to yield, after considerable effort, (46) (47) (48) (49)

  35. Where G is the mass flux with units of mass/(area time), and (50) Equation 50 relates the Mach numbers to the frictional losses in the pipe. The various energy contributions are identified. The compressibility term accounts for the change in velocity due to the expansion of the gas. Equations 49 and 50 are converted to a more convenient and useful form by replacing the Mach numbers with temperatures and pressures using Equations 46 through 48. (51) (52) kinetic energy compressibility pipe friction

  36. For most problems the pipe length (L), inside diameter (d), upstream temperature (T1) and pressure (P1), and downstream pressure (P2) are known. To compute the mass flux, G, the procedure is as follows. 1. Determine pipe roughness, e from Table 1. Compute e/d. 2. Determine the Fanning friction factor, f, from Equation 27. This assumes fully developed turbulent flow at high Reynolds numbers. This assumption can be checked later, but is normally valid. 3. Determine T2from Equation 51. 4. Compute the total mass flux, G, from Equation 52. For long pipes, or for large pressure differences across the pipe, he velocity of the gas can approach the sonic velocity. This case is shown in Figure 12. At the sonic velocity the flow will be choked. The gas velocity will remain at the sonic velocity, temperature, and pressure for the remainder of the pipe. For choked flow, Equations 46 through 50 are simplified by setting Ma2 = 1.0. The results are :

  37. (53) (54) (55) (56) (57) Choked flow occurs if the down stream pressure is less than Pchoked. This is checked using Equation 54.

  38. Figure 12 Adiabatic, choked flow of gas through a pipe. The maximum velocity reached is the sonic velocity of the gas

  39. For most problems involving choked, adiabatic flows, the pipe length (L), inside diameter (d), and upstream pressure (P1) and temperature (T1) are known. To compute the mass flux, G, the procedure is as follows. 1. Determine the Fanning friction factor, f, using Equation 27. This assumes fully developed turbulent flow at high Reynolds number. This assumption can be checked later, but is normally valid. 2. Determine Ma1, from Equation 57. 3. Determine the mass flux, Gchoked, from Equation 56. 4. Determine Pchoked from Equation 54 to confirm operation at choked conditions.

  40. Isothermal Flow Isothermal flow of gas in a pipe with friction is shown in Figure 13. For this case the gas velocity is assumed to be well below the sonic velocity of the gas. A pressure gradient across the pipe provides the driving force for the gas transport. As the gas expands through the pressure gradient the velocity must increase to maintain the same mass flowrate. The pressure at the end of the pipe is equal to the pressure of the surroundings. The temperature is constant across the entire pipe length. Isothermal flow is represented by the mechanical energy balance in the form shown in Equation 44. The following assumptions are valid for this case.

  41. is valid for gases, and form Equation 23, assuming constant f, and since no mechanical linkages are present. A total energy balance is not required since the temperature is constant.

  42. Figure 13 Isothermal, non-choked flow of gas through a pipe.

  43. Applying the above assumptions to Equation 44, and, after considerable manipulation (58) (59) (60) (61)

  44. where G is the mass flux with units of mass/(area time), and, (62) The various energy terms in Equation 62 have been identified. A more convenient form of Equation 62 is in terms of pressure instead of Mach numbers. This form is achieved by using Equations 58 through 60. The result is (63) kinetic energy pipe friction compressibility

  45. A typical problem is to determine the mass flux, G, given the pipe length (L), inside diameter (d), and upstream and downstream pressures (P1 and P2). The procedure is as follows. 1. Determine the Fanning friction factor, f, using Equation 27. This assumes fully developed turbulent flow at high Reynolds number. This assumption can be checked later, but is usually valid. 2. Compute the mass flux, G, from Equation 63. Levenspiel has shown that the maximum velocity possible during the isothermal flow of gas in a pipe is not the sonic velocity as in the adiabatic case. In terms of the Mach number, the maximum velocity is (64)

  46. This result is shown by starting with the mechanical energy balance and rearranging it into the following form. (65) the quantity -(dP/dL)--> when Ma --> 1/g. Thus, for choked flow in an isothermal pipe, as shown in Figure 14, the following equations apply.

  47. (66) (67) (68) (69) (70) where Gchoked is the mass flux with unit of mass/(area/time), and (71)

  48. Figure 14 Isothermal, choked flow of gas through a pipe. The maximum velocity reached is a/.

  49. For most typical problems the pipe length (L), inside diameter (d), upstream pressure (P1), and temperature (T) are known. The mass flux, G, is determined using the following procedure. 1. Determine the Fanning friction factor, f, using Equation 27. This assumes fully developed turbulent flow at high Reynolds number. This assumption can be checked later, but is usually valid. 2. Determine Ma1 from Equation 71. 3. Determine the mass flux, G, from Equation 70.

  50. 6. Flashing Liquids Liquids stored under pressure above their normal boiling point will partially flash into vapour following a leak, sometimes explosively. Flashing occurs so rapidly that the process is assumed to be adiabatic. The excess energy contained in the superheated liquid vaporizes the liquid and lower the temperature to the new boiling point. m = the mass of original liquid, Cp = heat capacity of the liquid (energy/mass deg), To = temperature of the liquid prior to depressurization Tb = boiling point of the liquid Q = excess energy contained in the superheated liquid

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