RBI Methodology - Consequence of Failure

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Introduction

The consequence analysis in an Newton RDMS is performed to aid in establishing a relative ranking of equipment items on the basis of risk.  The consequence analysis is a simplified, credible estimate of what might be expected to happen if a loss of containment were to occur in the equipment item being modeled.  The estimate is then converted to one of five consequence categories which provide a relative ranking of consequence of failure of the equipment item being analyzed in the program.

The consequence analysis method developed in this document has a demonstrated ability to provide the required discrimination between higher and lower consequence equipment items. The method is based upon the Environmental Protection Agency’s RMP OFFISTE CONSEQUENCE ANALYSIS GUIDANCE DOCUMENT published by the U.S. Environmental Protection Agency (EPA) on Mary 24, 1996 for distance to injury models for flammables and toxics.

Consequence Categories

There are up to four consequence categories included in the consequence of failure depending on the equipment type.  All equipment includes a calculated safety consequence and an optional manually entered production loss.  Storage tank bottoms can also include environmental cleanup cost.  Exchanger bundles can also include product leak cost.

The system determines safety consequence of failure for all equipment types except exchanger bundles from affected area depending on the fluid type.  The method to determine safety consequence and product leak cost for exchanger bundles is explained below.

In Newton RDMS, there are four types of Representative Fluids:

  • Flammable.
  • Toxic (i.e., inhalation toxic to humans).
  • Reactive (i.e., reacts with skin to cause injury).
  • Inert.

The affected area is converted to a Consequence Category based on the Table below.

The affected area for Flammable and Toxic fluids is calculated using methods published by EPA in "Risk Management Program Guidance for Offsite Consequence Analysis".

This EPA document does not address fluids that can cause injury to skin upon contact such as acids and bases.  Newton RDMS uses a modified version of the flammable liquid analysis to estimate pool size for Reactive fluids.

Fluids that are not Flammable, Toxic or Reactive are categorized as "Inert" and are assigned the lowest Consequence Category "E" unless the Burst model is activated.

Affected Area Range (square feet) Consequence Category
> 5,000,000 A
500,000 to 5,000,000 B
50,000 to 500,000 C
5,000 to 50,000 D
< 5,000 E

Release Parameters

  1. Fluid properties – Newton RDMS looks up the following fluid properties based on the Representative Fluid.
    • Molecular weight
    • Liquid density
    • Buoyancy (buoyant or dense)
    • Ideal gas heat capacities
    • Boiling point
    • Heat of combustion (Flammable fluids only)
    • Pool Fire Factor (Flammable fluids only)
    • Toxic end point (Toxic fluids only)
    • Liquid Factor Ambient (Toxic fluids only)
    • Liquid Factor Boiling (Toxic fluids only)
  2. Inventory – User enters the Inventory that represents the maximum available mass for release. Typical defaults are 40,000 lbs. if Initial State is Liquid or 10,000 lbs. if Initial State is Gas. The default values should be replaced by more accurate estimates for either very large volumes (e.g., storage tank, sphere, bullet, large columns) or very small volumes (e.g., filters). When calculating Inventory, consider the mass that may flow into the risk component from connected equipment as well as the effects of gravity, pumps and leaking valves. Refer to API 581, Part 3, section 4.4 for additional guidance.
  3. Leak Area – Newton RDMS looks up a frequency-weighted leak area based on the equipment type as shown in the Table below.
    Equipment Type Leak Area (square inches)
    ½” Pipe 0.049
    3/4" Pipe 0.049
    1" Pipe 0.110
    1.5" Pipe 0.150
    2" Pipe 0.193
    2.5" Pipe 0.256
    3" Pipe 0.318
    4" Pipe 0.442
    6" Pipe 0.994
    8" Pipe 1.230
    10" Pipe 1.480
    12" Pipe 1.770
    14" Pipe 1.920
    16" Pipe 2.070
    18" Pipe 2.070
    20" Pipe 2.240
    24" Pipe 2.410
    30" Pipe 3.140
    36" Pipe 3.970
    48" Pipe 4.910
    60" Pipe 7.070
    Pressure Vessel 8.300
    Filter 3.140
    Column 8.300
    Heat Exchanger Shell or Channel 8.300
    Heat Exchanger Tube 0.100
    Reactor 19.640
    Storage Tank 314.200
  4. Release type – In Newton RDMS, all releases are modeled as continuous, but release quantity is limited by either release duration or Inventory as explained below.
  5. If Initial State is Gas, then the following equation is used to calculate gas density.

    ``rho = 0.0936 xx MW xx frac{(OP + 14.7)}{(OT + 459.67)}``

    Where:

    ρ = gas density (lb/ft3)

    MW = molecular weight (g/ml)

    OP = operating pressure (psi)

    OP = operating temperature (F)

  6. Liquid release rate – Newton RDMS uses the following equation to calculate Liquid release rate.

    ``Q_L= C_d xx A xx sqrt (2 xx rho xx DP xx frac{g_c}{144} xx 60)``

    Where:

    QL = flammable liquid release rate (lb/min)

    Cd = discharge coefficient = 0.61 for liquids

    A = leak area (in2)

    ρ = density (lb/ft3), If Initial State is Liquid, then density is Liquid Density from RepFluid table. If Initial State is Gas, then density is Gas Density from previous step.

    DP = 96.75% of operating pressure (psig)

    gc = conversion factor from lbf to lb = 32.2 lb-ft/lbf-sec2

  7. Transition pressure – Newton RDMS uses the following equation to calculate the transition pressure and determine which equation to use for gas release rate. If the equipment's operating pressure is greater than the transition pressure then the equation for Sonic gas release rate is used; otherwise the Sub-sonic gas release rate equation is used.

    ``P_(trans)= P_a xx (frac{K + 1}{2})^(frac{K}{K - 1})``

    Where:

    Ptrans = transition pressure (psia)

    Pa = atmospheric pressure = 14.7 psia

    K = Cp/Cv

    Cp = ideal gas heat capacity at constant pressure (BTU/lb-mol °F)

    Cv = ideal gas heat capacity at constant volume (BTU/lb-mol °F)

  8. Sonic Gas release rate – Newton RDMS uses the following equation to calculate the Sonic gas release rate.

    ``W_g (sonic)= C_d xx A xx P xx sqrt (frac{K xx M}{R xx T} xx frac{g_c}{144} xx (frac{2}{K + 1})^(frac{K + 1}{K - 1)) ``

    Where:

    Wg (sonic) = gas discharge rate at sonic flow (lb/min)

    Cd = discharge coefficient = 0.9 for gas

    A = leak area (in2)

    P = upstream pressure = Operating Pressure + Pa (psia); Pa = atmospheric pressure = 14.7 psia

    K = Cp/Cv ; Cp = ideal gas heat capacity at constant pressure (BTU/lb-mol °F); Cv = ideal gas heat capacity at constant volume (BTU/lb-mol °F)

    M = molecular weight of Representative Fluid (lb/lb-mol)

    R = gas constant = 10.73 ft3-psia/lb- mol °R

    T = upstream temperature (°R) = Operating Temperature (°F) + 459.67

    gc = conversion factor from lbf to lb = 32.2 lb-ft/lbf-sec2

  9. Sub-sonic Gas release rate - Newton RDMS uses the following equation to calculate the Sub-sonic gas release rate.

    ``W_g ("subsonic")= C_d xx A xx P xx sqrt (frac{M}{R xx T} xx frac{g_c}{144} xx frac{2 xx K}{K - 1} xx (frac{P_a}{P})^(frac{2}{K}) xx [1 - (frac{P_a}{P})^(frac{K - 1}{K})]) ``

    Where:

    Wg (subsonic) = gas discharge rate at subsonic flow (lb/min)

    Cd = discharge coefficient = 0.9 for gas

    A = leak area (in2)

    P = upstream pressure = Operating Pressure + Pa (psia); Pa = atmospheric pressure = 14.7 psia

    K = Cp/Cv ; Cp = ideal gas heat capacity at constant pressure (BTU/lb-mol °F); Cv = ideal gas heat capacity at constant volume (BTU/lb-mol °F)

    M = molecular weight of Representative Fluid (lb/lb-mol)

    R = gas constant = 10.73 ft3-psia/lb- mol °R

    T = upstream temperature (°R) = Operating Temperature (°F) + 459.67

    gc = conversion factor from lbf to lb = 32.2 lb-ft/lbf-sec2

  10. Release Duration – Newton RDMS determines the release duration as the shorter of the sum of detection time & isolation time or the deinventory time which is the Inventory divided by the appropriate release rate (i.e., liquid or gas).
  11. Leak Quantity - Newton RDMS calculates Leak Quantity by multiplying the appropriate release rate (i.e., liquid or gas) by Release Duration. This approach assumes release rate stays constant which is a conservative assumption. Leak Quantity will not exceed Inventory.
  12. Final phase – Newton RDMS uses the following Table to determine the Final phase.
    Fluid phase at Normal operating/storage conditions Fluid phase at Ambient (after release) conditions Final Phase
    Gas Gas Gas
    Gas Liquid Gas
    Liquid Gas Gas unless fluid Boiling Point is greater than 100 degrees F; then Liquid
    Liquid Liquid Liquid

Flammable Affected Area

  1. Gas Final Phase distance to injury – Flammable gas releases are assumed to form a vapor cloud and 10% of the cloud (i.e., 0.10 yield factor) is assumed to participate in an explosion. Newton RDMS calculates the distance to injury from an overpressure of 1 psi using the following equation based on the TNT equivalency method.

    ``D = [0.0081 xx (0.1 xx W_f xx frac{HC_f}{HC_(TNT)})^frac{1}{3}] xx 5280``

    Where:

    D = distance to injury (ft.)

    Wf = Leak Quantity (i.e., weight of flammable substance in lbs.)

    HCf = heat of combustion of Representative Fluid (J/g)

    HCTNT = heat of combustion of trinitrotoluene (i.e., TNT) = 4680 J/g

  2. Liquid Final Phase distance to injury – Flammable liquid releases are assumed to form a liquid pool approximately 1 cm deep (i.e., 0.0325 ft) and the pool ignites. Newton RDMS calculates the distance to injury from thermal radiation at 5000 W/m2 and 40-second exposure (i.e., resulting in second degree burns) using the following equation.

    ``D = PFF xx sqrt A``

    Where:

    D = distance to injury (ft)

    PFF = Pool Fire Factor of Representative Fluid

    ``A = frac{L_Q}{0.0325 xx rho}``

    Where:

    A = liquid pool area (ft2). If the user indicates a liquid release will be contained by a dike (i.e., containment wall), then the pool area is set to the "Diked Area" entered by the user.

    LQ = Leak Quantity (lb)

    ρ = liquid density of Representative Fluid (lb/ft3)

  3. Probability of ignition (PIG) – Newton RDMS sets the PIG to the probability of ignition at Flash Point temperature of Representative Fluid (PIGF) when the Operating Temperature (TOP) is below the Flash Point temperature of Representative Fluid (TLF).  The program sets PIG to 1.0 when the Operating Temperature (TOP) is equal to or above Auto Ignition Temperature (TAUTO) of Representative Fluid or when the user indicates "Near Ignition Source".  Otherwise, Newton RDMS calculates the probability of ignition using the following equation.

    ``P_(IG) = P_(IGF) + [(frac{T_(OP) - T_(FL)}{T_(AUTO) - T_(FL)}) xx (1 - P_(IGF))]``

    Where:

    PIG = probability of ignition

    PIGF = probability of ignition at Flash Point temperature of Representative Fluid

    TOP = operating temperature (°F)

    TFL = Flash Point temperature of Representative Fluid (°F)

    TAUTO = Auto Ignition Temperature of Representative Fluid (°F)

  4. Flammable affected area – Newton RDMS calculates the Flammable affected area using the following equation.

    ``"FAA" = P_(IG) xx pi xx D^2``

    Where:

    FAA = Flammable Affected Area (ft2)

    PIG = probability of ignition

    D = distance to injury (ft) and diameter of a circle

Reactive Affected Area

Reactive fluids are those that cause injury by contact such as acid or strong bases. This methodology was developed by Capstone based on EPA approach for flammable liquid releases. Reactive fluids are assumed to be a liquid and form a pool approximately 1 cm deep (i.e., 0.0325 ft). Newton RDMS calculates the Reactive fluid affected area by setting it equal to the liquid pool area using the following equation.

``A = frac{L_Q}{(0.0325 xx rho)}``

Where:

A = liquid pool area (ft2). If the user indicates a liquid release will be contained by a dike (i.e., containment wall), then the pool area is set to the "Diked Area" entered by the user. 0.03281

LQ = Leak Quantity (lbs)

ρ = liquid density of Representative Fluid (lb/ft3)

 

Toxic Affected Area

  1. Toxic Liquid evaporation rate – For toxic Liquid final phase, Newton RDMS assumes the Leak Quantity forms a pool approximately 1 cm deep (i.e., 0.0325 ft) and then evaporates to the air causing an inhalation hazard. The system calculates the Toxic Liquid evaporation rate using the following equation.

    ``Q_(LT) = (1.4 xx LF_x xx A) * 60

    Where:

    QTL = toxic liquid evaporation rate (lb/min). For Toxic Mixtures, the toxic liquid evaporation rate is multiplied by the percent toxic.

    LFX = Liquid Factor of Representative Fluid.  When Operating Temperature is less than 100 °F, Newton RDMS uses Liquid Factor Ambient (LFA).  When Operating Temperature is equal to or greater than 100 °F, AllAssets uses Liquid Factor Boiling (LFB).

    ``A = frac{L_Q}{(0.0325 xx rho)}``

    Where:

    A = liquid pool area (ft2). If the user indicates a liquid release will be contained by a dike (i.e., containment wall), then the pool area is set to the "Diked Area" entered by the user.

    LQ = Leak Quantity (lbs)

    ρ = liquid density of Representative Fluid (lb/ft3)

  2. Toxic Release Duration – Newton RDMS uses the Toxic release duration to determine which distance to injury lookup table to use.  The Toxic release duration is calculated by dividing Leak Quantity (LQ) by the Toxic Liquid evaporation rate (QTL).  This value is not shown on the Newton RDMS Consequence screen.
  3. Toxic gas release rate – For toxic Gas final phase, the system selects one of several release rates depending on whether the toxic gas is the Representative Fluid or Toxic Mixture.
    • If Toxic is Representative Fluid: Smaller of inventory-limited rate or Gas release rate as defined in Sonic or Sub-sonic gas release rate. Inventory-Limited rate = Inventory / Toxic Release duration
    • If Toxic is Toxic Mixture:  Smaller of % toxic multiplied by inventory-limited rate or % toxic multiplied by Gas release rate as defined in Sonic or Sub-sonic gas release rate.
  4. Determine Toxic lookup table – The application uses four lookup tables from EPA's publication "Risk Management Program Guidance for Offsite Consequence Analysis" to determine Toxic distance to injury.  Newton RDMS assumes the topography is "rural" and determines the lookup table based on Toxic release duration and buoyancy as shown in the Table below.
    Lookup Table Release Duration Buoyancy (see note)
    1 10 minutes or less Buoyant
    2 Greater than 10 minutes (EPA's 60-minute table) Buoyant
    3 10 minutes or less Dense
    4 Greater than 10 minutes (EPA's 60-minute table) Dense

    NOTE: Buoyancy is one of the fluid properties for Representative Fluids.

  5. Toxic distance to injury – Newton RDMS sets Toxic distance to injury equal to the EPA lookup value "distance to toxic endpoint".  Toxic endpoint is one of the fluid properties for Representative Fluids.  Lookup tables are used differently depending on whether the fluid is buoyant or dense.
    • If fluid is buoyant, divide "release rate" by Toxic Endpoint to find the range in the first column that includes this value then lookup the corresponding distance to toxic endpoint (i.e. Toxic distance to injury).  The "release rate" is either Toxic gas release rate or Toxic liquid evaporation rate.
    • If fluid is dense, find the endpoint column closest to the Toxic endpoint and then find the release rate row closest to the "release rate" (i.e. Toxic gas release rate or Toxic liquid evaporation rate). The intersection of column and row is the distance to toxic endpoint (i.e. Toxic distance to injury).
      • If the Toxic endpoint is between two column values, then choose the smaller column value if Toxic endpoint is less than or equal to the average of two values. 
      • If the "release rate" is between two row values, then choose the larger row value if "release rate" is greater than or equal to the average of two values.
  6. Toxic affected area – Newton RDMS calculates the Toxic affected area using the following equation.

    ``"TAA" = frac{pi}{40} xx D^2``

    Where:

    TAA = Toxic Affected Area (ft2)

    D = distance to injury (ft) and the major axis of an ellipse; EPA distance to toxic endpoint in miles multiplied by 5280 ft/mile.

    NOTE.  ``"Area of ellipse" = pi xx a xx b`` where “a” = one-half Major Axis and “b” = one-half Minor Axis. Major Axis set equal to Distance to injury (D) so a = D/2. Newton RDMS assumes 10:1 ratio so Minor axis = 1/10th of Major Axis. Minor axis = D/10 which also equals 2b. Therefore b = D/20.

    ``Area = pi xx frac{D}{2} xx frac{D}{20} = pi xx frac{D^2}{40}``

Toxic Lookup Table 1 – Buoyant for 10-minute release

Release Rate/Endpoint

[(lbs./min)/(mg/L)]

Distance to Endpoint

(miles)

 

Release Rate/Endpoint

[(lbs./min)/(mg/L)]

Distance to Endpoint

(miles)

0 ‑ 4.4 0.06   16,000 ‑ 18,000 4.8
4.4 ‑ 37 0.19   18,000 ‑ 19,000 5.0
37 ‑ 97 0.31   19,000 ‑ 21,000 5.2
97 ‑ 180 0.43   21,000 ‑ 23,000 5.4
180 ‑ 340 0.62   23,000 ‑ 24,000 5.6
340 ‑ 530 0.81   24,000 ‑ 26,000 5.8
530 ‑ 760 0.99   26,000 ‑ 28,000 6.0
760 ‑ 1,000 1.2   28,000 ‑ 29,600 6.2
1,000 ‑ 1,500 1.4   29,600 ‑ 35,600 6.8
1,500 ‑ 1,900 1.6   35,600 ‑ 42,000 7.5
1,900 ‑ 2,400 1.8   42,000 ‑ 48,800 8.1
2,400 ‑ 2,900 2.0   48,800 ‑ 56,000 8.7
2,900 ‑ 3,500 2.2   56,000 ‑ 63,600 9.3
3,500 ‑ 4,400 2.4   63,600 ‑ 71,500 9.9
4,400 ‑ 5,100 2.6   71,500 ‑ 88,500 11
5,100 ‑ 5,900 2.8   88,500 ‑ 107,000 12
5,900 ‑ 6,800 3.0   107,000 ‑ 126,000 14
6,800 ‑ 7,700 3.2   126,000 ‑ 147,000 15
7,700 ‑ 9,000 3.4   147,000 ‑ 169,000 16
9,000 ‑ 10,000 3.6   169,000 ‑ 191,000 17
10,000 ‑ 11,000 3.8   191,000 ‑ 215,000 19
11,000 ‑ 12,000 4.0   215,000 ‑ 279,000 22
12,000 ‑ 14,000 4.2   279,000 ‑ 347,000 25
14,000 ‑ 15,000 4.4   >347,000 >25
15,000 ‑ 16,000 4.6      

 Toxic Lookup Table 2 – Buoyant for 60-minute release

Release Rate/Endpoint

[(lbs./min)/(mg/L)]

Distance to Endpoint

(miles)

 

Release Rate/Endpoint

[(lbs./min)/(mg/L)]

Distance to Endpoint

(miles)

0 ‑ 5.5 0.06   7,400 ‑ 7,700 4.8
5.5 ‑ 46 0.19   7,700 ‑ 8,100 5.0
46 ‑ 120 0.31   8,100 ‑ 8,500 5.2
120 ‑ 220 0.43   8,500 ‑ 8,900 5.4
220 ‑ 420 0.62   8,900 ‑ 9,200 5.6
420 ‑ 650 0.81   9,200 ‑ 9,600 5.8
650 ‑ 910 0.99   9,600 ‑ 10,000 6.0
910 ‑ 1,200 1.2   10,000 ‑ 10,400 6.2
1,200 ‑ 1,600 1.4   10,400 ‑ 11,700 6.8
1,600 ‑ 1,900 1.6   11,700 ‑ 13,100 7.5
1,900 ‑ 2,300 1.8   13,100 ‑ 14,500 8.1
2,300 ‑ 2,600 2.0   14,500 ‑ 15,900 8.7
2,600 ‑ 2,900 2.2   15,900 ‑ 17,500 9.3
2,900 ‑ 3,400 2.4   17,500 ‑ 19,100 9.9
3,400 ‑ 3,700 2.6   19,100 ‑ 22,600 11
3,700 ‑ 4,100 2.8   22,600 ‑ 26,300 12
4,100 ‑ 4,400 3.0   26,300 ‑ 30,300 14
4,400 ‑ 4,800 3.2   30,300 ‑ 34,500 15
4,800 ‑ 5,200 3.4   34,500 ‑ 38,900 16
5,200 ‑ 5,600 3.6   38,900 ‑ 43,600 17
5,600 ‑ 5,900 3.8   43,600 ‑ 48,400 19
5,900 ‑ 6,200 4.0   48,400 ‑ 61,500 22
6,200 ‑ 6,700 4.2   61,500 ‑ 75,600 25
6,700 ‑ 7,000 4.4   >75,600 >25
7,000 ‑ 7,400 4.6      

 Toxic Lookup Table 3 – Dense for 10-minute release

Release Rate   Endpoint Column (mg/L)
(lbs./min) 0.0004 0.0007 0.001 0.002 0.0035 0.005 0.0075 0.01 0.02 0.035 0.05 0.075 0.1 0.25 0.5 0.75
    Distance to toxic endpoint (Miles)
1 2.2 1.7 1.5 1.1 0.81 0.68 0.53 0.46 0.31 0.23 0.19 0.15 0.12 0.06 # #
2 3.0 2.4 2.1 1.5 1.1 0.93 0.74 0.68 0.45 0.33 0.27 0.21 0.18 0.11 <0.06 <0.06
5 4.8 3.7 3.0 2.2 1.7 1.5 1.2 0.99 0.74 0.53 0.43 0.34 0.29 0.16 0.11 0.07
10 6.8 5.0 4.2 3.0 2.4 2.1 1.7 1.4 0.99 0.74 0.62 0.50 0.42 0.24 0.15 0.12
30 11 8.7 6.8 5.2 3.9 3.4 2.8 2.4 1.7 1.3 1.1 0.87 0.74 0.42 0.27 0.20
50 14 11 9.3 6.8 5.0 4.2 3.5 3.0 2.2 1.7 1.4 1.1 0.93 0.56 0.35 0.27
100 19 15 12 8.7 6.8 5.8 4.8 4.2 2.9 2.2 1.9 1.6 1.3 0.81 0.51 0.38
150 24 18 15 11 8.1 6.8 5.7 5.0 3.6 2.7 2.3 1.9 1.6 0.93 0.61 0.47
250 >25 22 19 14 11 8.7 7.4 6.2 4.5 3.4 2.8 2.3 2.0 1.2 0.81 0.60
500 * >25 >25 19 14 12 9.9 8.7 6.2 4.7 3.8 3.1 2.7 1.6 1.1 0.87
750 * * * 23 17 15 12 11 7.4 5.5 4.5 3.7 3.2 1.9 1.3 0.99
1000 * * * >25 20 17 14 12 8.1 6.2 5.2 4.2 3.6 2.2 1.4 1.1
1500 * * * * 24 20 16 14 9.9 7.4 6.2 5.0 4.3 2.5 1.7 1.3
2000 * * * * >25 23 19 16 11 8.7 6.8 5.6 4.8 2.9 1.9 1.5
2500 * * * * * >25 20 18 12 9.3 8.1 6.2 5.3 3.2 2.1 1.6
3000 * * * * * * 23 20 14 9.9 8.7 6.8 5.6 3.4 2.2 1.7
4000 * * * * * * >25 22 16 11 9.3 7.4 6.2 3.8 2.5 2.0
5000 * * * * * * * 25 17 13 11 8.7 6.8 4.2 2.7 2.1
7500 * * * * * * * >25 20 15 12 9.9 8.7 4.9 3.2 2.5
10000 * * * * * * * * 24 17 14 11 9.3 5.5 3.6 2.8
15000 * * * * * * * * >25 20 17 13 11 6.2 4.2 3.2
20000 * * * * * * * * * 23 19 15 12 7.4 4.7 3.7

Toxic Lookup Table 4 – Dense for 60-minute release

Release Rate   Endpoint column (mg/L)
(lbs./min) 0.0004 0.0007 0.001 0.002 0.0035 0.005 0.0075 0.01 0.02 0.035 0.05 0.075 0.1 0.25 0.5 0.75
    Distance to toxic endpoint (Miles)
1 3.7 2.7 2.2 1.4 0.99 0.81 0.62 0.53 0.34 0.24 0.19 0.14 0.12 <0.06 # #
2 5.3 4.0 3.2 2.2 1.6 1.2 0.99 0.81 0.53 0.37 0.29 0.22 0.18 0.09 <0.06 <0.06
5 8.7 6.8 5.3 3.7 2.7 2.2 1.7 1.4 0.93 0.62 0.51 0.39 0.32 0.17 0.10 0.07
10 12 9.3 8.1 5.3 4.0 3.3 2.7 2.2 1.4 0.99 0.81 0.60 0.50 0.26 0.16 0.11
30 22 16 14 9.9 7.4 6.1 4.9 4.1 2.9 2.1 1.6 1.2 0.99 0.52 0.31 0.22
50 >25 21 18 12 9.3 8.1 6.2 5.4 3.8 2.7 2.2 1.7 1.4 0.74 0.43 0.31
100 * >25 >25 18 13 11 9.3 7.4 5.5 4.0 3.2 2.5 2.1 1.1 0.68 0.48
150 * * * 22 17 14 11 9.9 6.8 4.9 4.0 3.1 2.7 1.4 0.87 0.61
250 * * * >25 22 18 14 12 8.7 6.2 5.2 4.1 3.5 1.9 1.2 0.87
500 * * * * >25 25 20 17 12 9.3 7.4 5.8 5.0 2.9 1.8 1.3
750 * * * * * >25 25 22 15 11 9.3 7.4 6.1 3.5 2.2 1.7
1000 * * * * * * >25 25 17 12 11 8.1 6.8 4.0 2.6 2.0
1500 * * * * * * * >25 20 16 12 9.9 8.7 5.0 3.2 2.5
2000 * * * * * * * * 24 17 14 11 9.9 5.7 3.7 2.9
2500 * * * * * * * * >25 20 16 13 11 6.2 4.2 3.2
3000 * * * * * * * * * 21 17 14 12 6.8 4.5 3.5
4000 * * * * * * * * * 24 20 16 14 8.1 5.2 4.0
5000 * * * * * * * * * >25 22 17 15 8.7 5.7 4.4
7500 * * * * * * * * * * >25 21 18 11 6.8 5.2
10000 * * * * * * * * * * * 24 20 12 7.4 6.0
15000 * * * * * * * * * * * >25 24 14 9.3 6.8
20000 * * * * * * * * * * * * >25 16 9.9 8.1

 

Burst Affected Area

The Burst model is based on methodology published by CCPS. This model is activated by a combination of three conditions; Representative Fluid is Inert, initial state is Gas and burst Volume is entered.

  1. Burst energy – Newton RDMS calculates the burst energy using the following equation.

    ``E = frac{(( P_1 - P_0) xx V)}{gamma - 1}``

    Where:

    E = burst energy (MJ)

    P1 = burst pressure = 4 * Design Pressure (bar)

    P0 = ambient pressure = 1.01 bar

    γ = heat capacity ratio = 1.1 for Steam and 1.4 for Air, Oxygen and Nitrogen

    V = burst volume (m3)

  2. Distance to injury – Newton RDMS calculates the distance to injury from 1 psia overpressure using the following equation.

    ``D = frac{R_S}{(frac{P_0}{E})^frac{1}{3}}``

    Where:

    D = burst distance to injury (m), multiply by 3.281 to convert m to ft

    RS = scaled distance = 3.1

    P0 = ambient pressure = 1.01 bar

    E = burst energy (MJ)

  3. Burst affected area – Newton RDMS calculates the Burst affected area using the following equation.

    ``"BAA" = pi xx D^2``

    Where:

    BAA = Burst Affected Area (ft2)

    D = distance to injury (ft) and the diameter of a circle; burst distance to injury in meters multiplied by 3.281 ft/m.

Inert

Unless the Burst model is activated, Inert fluids are assigned Consequence Category "E".

Production Loss

Newton RDMS does not calculate production loss so it must be entered manually by selecting the Consequence Category which does not require defining a monetary value.

If a customer wants to estimate a monetary value before selecting the Consequence Category, then the following is one way to calculate the cost of production loss.  The Table below can then be used to determine the Production Loss Consequence Category.

``PLC = %UD xx AvgUC xx HrsD``

Where:

PLC = Production Loss Cost ($)

%UD = % Unit Down if equipment not functioning

AvgUC = Average Cost per Hour for Unit Downtime ($/hr)

HrsD = Number of hours unit is down (stream-to-stream) when equipment not functioning (hrs.)

Suggested Ranges for Production Loss ($) Consequence Category
> 20,000,000 A
2,000,000 to 20,000,000 B
200,000 to 2,000,000 C
20,000 to 200,000 D
< 20,000 E

Tank Bottom Environmental Cleanup Cost

Newton RDMS calculates environmental cleanup cost for storage tank bottoms based on methodology developed by Capstone. The cleanup cost is then used to determine the Environmental cleanup cost Consequence Category according to the Table below.

  1. Foundation type – No environmental cleanup cost is determined when the tank has a double floor or when the floor is fully supported by a concrete pad. Environmental cleanup cost is only determined for the following foundation types: clay, silt, sand or gravel.
  2. Persistent fluid – No environmental cleanup cost is determined when the stored fluid is not persistent (i.e. remains liquid after release). Environmental cleanup cost is only determined for Persistent fluids.
  3. Corrosion category – The corrosion category depends on the sum of the internal and underside corrosion rates according to the Table below.
    Tank Bottom Corrosion Category
    Total Corrosion Rate (mils per year) Corrosion Category
    < 5 Low
    5 to 10 Medium
    > 10 High
  4. Average leak size – The average leak size starts as a quarter inch hole (0.25 in2) and increases over time based on the corrosion category and tank inspection interval as follows:

    ``ALS = 0.25 xx 2^(frac{"TankInspIntvl"}{"CorrF"})``

    Where:

    ALS = Average leak size (in2)

    0.25 = initial leak size (in2)

    TankInspIntvl = internal tank inspection interval entered by user (yrs)

    CorrF = factor based on corrosion category. If corrosion category is Low, CorrF = 20. If corrosion category is Medium, CorrF = 10. If corrosion category is High, CorrF = 5.

  5. Average leak rate – The average leak rate is determined as follows based on the average leak diameter and foundation type:

    ``"ALF" = FF xx ALD``

    Where:

    ALR = Average leak rate (gal/day)

    FF = factor based on foundation type. If foundation is Clay, FF = 0.15. If foundation is Silt, FF = 24. If foundation is Sand, FF = 29. If foundation is Gravel, FF = 192.

    ALD = Average leak diameter as determined above (inches)

  6. Unit cleanup cost – The Unit cleanup cost entered by user ($/gal).

  7. Environmental cleanup cost – The environmental cleanup cost is determined as follows:

    ``"ECC" = UC xx ALR xx 365 xx "TankInspIntvl" xx 0.5``

    Where:

    ECC = Environmental cleanup cost ($)

    UC = Unit cleanup cost entered by user ($/gal)

    ALR = Average leak rate as determined above (gal/day)

    365 = number of days per year

    TankInspIntvl = internal tank inspection interval entered by user (yrs.)

    0.5 = one-half of the inspection interval

  8. Environmental cleanup Consequence Category – The environmental cleanup cost is then used to determine the Environmental cleanup Consequence Category according to the Table below. NOTE: The following dollar value ranges are set inside the tank bottom consequence model.

    Environmental Cleanup Cost Range ($) Consequence Category
    > 10,000,000 A
    1,000,000 to 10,000,000 B
    100,000 to 1,000,000 C
    10,000 to 100,000 D
    < 10,000 E

Exchanger Bundle Consequence

Safety consequence of failure

Newton RDMS determines safety consequence of failure for exchanger bundles based on the following method developed by Capstone:

  1. Leak direction – The direction of leak from a tube in the bundle is from the higher pressure side to lower pressure side based on operating pressures for the shell and channel sides.  If the two pressures are equal then leak direction is N/A.
  2. Delta pressure – The delta pressure is the absolute value of the difference between shell and channel side operating pressures.
  3. Fluid properties – The system looks up the following fluid properties for the Representative Fluid on the high-pressure side of the exchanger.
    • Molecular weight
    • Liquid density
    • Ideal gas heat capacities
  4. Leak Area – Newton RDMS looks up a leak area based on the equipment type as shown here which is 0.1 square inches for exchanger tubes.
  5. Initial leak rate – The initial leak rate is determined for the Representative Fluid on the high-pressure side of the exchanger using a method very similar to step "Release Parameters". The exceptions for bundles are noted in the following steps.
  6. Liquid release rate – Newton RDMS uses the following equation to calculate Liquid release rate.

    ``Q_L = C_d xx A xx sqrt(2 xx rho xx DP xx frac{g_c}{144}) xx 60``

    Where:

    QL = flammable liquid release rate (lb/min)

    Cd = discharge coefficient = 0.61 for liquids

    A = leak area (in2) = Pi/4 * (initial tube wall thickness)2; this is an exception for bundles.

    ρ = liquid density of Representative Fluid (lb/ft3)

    DP = delta pressure (psig); this is an exception for bundles. If DP is zero then liquid release rate is N/A.

    gc = conversion factor from lbf to lb = 32.2 lb-ft/lbf-sec2

  7. Transition pressure – Newton RDMS uses the following equation to calculate the transition pressure and determine which equation to use for gas release rate. If the delta pressure is greater than the transition pressure then the equation for Sonic gas release rate is used; otherwise the Sub-sonic gas release rate equation is used.

    ``P_(trans) = P_a xx (frac{K + 1}{2})^frac{K}{K - 1}``

    Where:

    Ptrans = transition pressure (psia)

    Pa = operating pressure of the low-pressure side of the bundle; this is an exception for bundles.

    K = Cp/Cv

    Cp = ideal gas heat capacity at constant pressure (BTU/lb-mol °F)

    Cv = ideal gas heat capacity at constant volume (BTU/lb-mol °F)

  8. Sonic Gas release rate – AllAssets uses the following equation to calculate the Sonic gas release rate.

    ``W_g(sonic) = C_d xx A xx P xx sqrt (frac{K xx M}{R xx T} xx frac{g_c}{144} xx (frac{2}{K + 1})^frac{K + 1}{K - 1})``

    Where:

    Wg (sonic) = gas discharge rate at sonic flow (lb/min)

    Cd = discharge coefficient = 0.9 for gas

    A = leak area (in2) = Pi/4 * (initial tube wall thickness)2; this is an exception for bundles.

    P = delta pressure (psig); this is an exception for bundles. If DP is zero then sonic gas release rate is N/A.

    K = Cp/Cv ; Cp = ideal gas heat capacity at constant pressure (BTU/lb-mol °F); Cv = ideal gas heat capacity at constant volume (BTU/lb-mol °F)

    M = molecular weight of Representative Fluid (lb/lb-mol)

    R = gas constant = 10.73 ft3-psia/lb- mol °R

    T = upstream temperature (°R) = Operating Temperature (°F) + 459.67

    gc = conversion factor from lbf to lb = 32.2 lb-ft/lbf-sec2

  9. Sub-sonic Gas release rate - Newton RDMS uses the following equation to calculate the Sub-sonic gas release rate.

    ``W_g ("subsonic")= C_d xx A xx P xx sqrt (frac{M}{R xx T} xx frac{g_c}{144} xx frac{2 xx K}{K - 1} xx (frac{P_a}{P})^(frac{2}{K}) xx [1 - (frac{P_a}{P})^(frac{K - 1}{K})]) ``

    Where:

    Wg (subsonic) = gas discharge rate at subsonic flow (lb/min)

    Cd = discharge coefficient = 0.9 for gas

    A = leak area (in2)

    P = upstream pressure = Operating Pressure + Pa (psia); Pa = atmospheric pressure = 14.7 psia

    K = Cp/Cv ; Cp = ideal gas heat capacity at constant pressure (BTU/lb-mol °F); Cv = ideal gas heat capacity at constant volume (BTU/lb-mol °F)

    M = molecular weight of Representative Fluid (lb/lb-mol)

    R = gas constant = 10.73 ft3-psia/lb- mol °R

    T = upstream temperature (°R) = Operating Temperature (°F) + 459.67

    gc = conversion factor from lbf to lb = 32.2 lb-ft/lbf-sec2

  10. Toxic mixture release rate – If the high-pressure side contains a toxic mixture, the toxic mixture release rate is the product of the initial leak rate (steps 5 to 9 above) and the percent toxic; otherwise, the toxic mixture release rate is N/A.

  11. Fluid final state – The user selects the fluid final state for shell side and channel side, either Liquid or Gas.

  12. Flammable leak type - The user selects the flammable leak type from the following choices when the high-pressure side has a flammable Representative Fluid or a toxic mixture:

    • Leak could cause a catastrophic loss of containment or violent chemical reaction
    • Flammable HC leak into utility system (NOTE: HC = hydrocarbon)
    • Utility leak into a HC system
    • N/A
  13. Toxic leak type – The user selects the toxic leak type from the following choices when the high-pressure side has a toxic Representative Fluid or a toxic mixture:
    • Toxic leak could cause a catastrophic loss of containment or violent chemical reaction
    • Toxic leak into a utility system
    • Toxic leak into process system
    • Leak into a toxic system
    • N/A
  14. Reactive or Inert fluids – If the high-pressure side Representative Fluid is Reactive or Inert, the only case when a safety consequence is determined is when a toxic mixture exists.  In this case, only the toxic consequence is determined.
  15. Flammable leak rate category – If the Representative Fluid is flammable and the initial leak rate is greater than or equal to 100 lb/min, then the flammable leak rate category is Major; otherwise it is Minor.
  16. Toxic leak rate category – If the Representative Fluid is toxic and the initial leak rate is greater than or equal to 5 lb/min, then the toxic leak rate category is Major; otherwise it is Minor. If the leak contains a toxic mixture and the toxic mixture leak rate is greater than or equal to 5 lb/min, then the toxic leak rate category is Major; otherwise it is Minor.
  17. Flammable Consequence Category – The flammable Consequence Category is determined based on the following Table where the Fluid Final State is from the high-pressure side:
    Flammable Leak Type Leak Rate Category Fluid Final State Consequence Category
    Leak could cause a catastrophic loss of containment or violent chemical reaction Major or Minor Liquid or Gas A
    Flammable HC leak into utility system Major Gas B
    Minor Gas C
    Major Liquid C
    Minor Liquid D
    Utility leak into a HC system Major Liquid or Gas D
    Minor Liquid or Gas E
  18. Toxic Consequence Category – The toxic Consequence Category is determined based on the following Table where the Fluid Final State is from the high-pressure side:
    Toxic Leak Type Leak Rate Category Fluid Final State Consequence Category
    Toxic leak could cause a catastrophic loss of containment or violent chemical reaction Major or Minor Liquid or Gas A
    Toxic leak into a utility system Major Liquid or Gas A
    Minor Liquid or Gas B
    Toxic leak into process system Major Liquid or Gas B
    Minor Liquid or Gas C
    Leak into a toxic system Major or Minor Liquid or Gas D

Product leak consequence

Newton RDMS determines bundle product leak consequence as follows based on methodology developed by Capstone:

  1. Corrosion category – The corrosion category depends on the sum of the shell side and channel side rates according to the Table below.
    Total Corrosion Rate (mils per year) Corrosion Category
    < 5 Low
    5 to 10 Medium
    > 10 High
  2. Time to detect leak – The user enters the time to detect a bundle leak which is recommended to be the bundle inspection interval.
  3. Average leak diameter – The average leak diameter starts as 0.1 inch diameter hole and increases over time based on the corrosion category and bundle inspection interval as follows:

    ``ALD = 0.1 xx 2^frac{"DetectLeakTime"}{"CorrF"}``

    Where:

    ALD = Average leak diameter (inches)

    0.1 = initial hole diameter (inches)

    DetectLeakTime = time to detect a leak entered by user which is recommended to be the bundle inspection interval (yrs)

    CorrF = factor based on corrosion category. If corrosion category is Low, CorrF = 10. If corrosion category is Medium, CorrF = 5. If corrosion category is High, CorrF = 3.33.

  4. Average leak rate – The average leak rate is calculated by following steps 5 to 9 in the previous section but substitute the average leak diameter for initial tube wall thickness in the release equations.
  5. Unit value of leaking product – The user enters the unit value of leaking product ($/lb).
  6. Value of lost product – The value of lost product is calculated as follows:

    ``VL = UV xx AvgLR xx DT xx 365/2``

    Where:

    VL = value of lost product ($)

    UV = unit value of leaking product ($/lb)

    AvgLR = average leak rate (lb/min)

    DT = time to detect leak
  7. Product Leak Consequence Category– The product leak Consequence Category is determined based on the value of lost product according to following Table. NOTE: Dollar value ranges are set inside the bundle consequence model.
    Value of Lost Product ($) Consequence Category
    > 10,000,000 A
    1,000,000 to 10,000,000 B
    100,000 to 1,000,000 C
    10,000 to 100,000 D
    < 10,000 E
  8. Combined bundle Consequence Category – The combined bundle Consequence Category is the worst consequence from the four possible values; flammable safety, toxic safety, production loss and product leak.

Relief Devices

Failure on demand rather than loss of containment that is determined based on possibility of corrosion or fouling using method developed by Capstone.

A four-step process described in the following sections determines the potential for damage.

EVALUATE THE POTENTIAL FOR FOULING

The potential for fouling is rated using the following scale (be sure to consider upset conditions):

  • Low = No expected potential for fouling (Fouling almost never occurs)
  • Medium = Minor potential for fouling (Some fouling seen in 2-3 years of service)
  • High = Significant potential for fouling (Fouls to the point of degraded capacity within 1-2 years)
  • Very High = Service (or similar service) known to have fouling problems (Fouls to the point of degraded capacity in less than a year)

In determining the fouling potential, the following steps should be completed:

  1. Process Review (Discuss with operations).
    • Polymerization Potential (Very High)
    • Stream contains solids - slurry, coke, catalyst (High/Very High)
    • Corrosion products present - scale, reaction products
    • Treatment chemicals or other suspended solids that may precipitate
    • Fouling that can occur due to upset conditions such as catalyst, temperature, etc.
  2. Review Inspection Records (Rework)
    • Evidence of fouling or corrosion
    • As received “pop” tests results

If a rupture disk protects the relief valve, reduce the fouling potential rating by one level. The credit for a rupture disk will be applied only if the space between the disk and the inlet of the valve has a suitable pressure tell-tale indicator that is monitored at least monthly.

EVALUATE THE POTENTIAL FOR CORROSION

The potential for corrosion is rated on the following scale:        

Rating Equipment Corrosion Rate (Inches/year)
Low <= 0.001
Medium >0.001 & <= 0.005
High >0.005 & <= 0.010
Very High > 0.010

Factors for adjustment:

  • Rupture disk protected = down one rating (The credit for a rupture disk will be applied only if the space between the disk and the inlet of the valve has a suitable pressure tell-tale indicator that is monitored at least monthly.)
  • Bellows valve or Pilot Operated Relief Valve Design= down one rating (Do not combine 1 & 2)
  • Higher Alloy Materials on Internal Parts = down one rating
  • Discharges to the atmosphere = up one level (i.e., Low becomes Medium, Medium becomes High, etc.)

DETERMINE THE DETERIORATION POTENTIAL

The Deterioration Potential is the combination of the Fouling Potential and the Corrosion Potential as determined by the following:

Result of Evaluations Deterioration Potential
One potential is higher than the other one Deterioration Potential = Highest potential
Both potentials are Low Deterioration Potential = Low
Both potentials are Medium Deterioration Potential = High
Both potentials are High Deterioration Potential = Very High
Both potentials are Very High Deterioration Potential = Very High

CALCULATE THE DETERIORATION FACTOR

The Deterioration Factor is calculated by selecting the highest Deterioration Potential (Fouling or Corrosion) and by using the appropriate Equation below:

Deterioration Factor Very High Potential = 10 (Years/1)

Deterioration Factor High Potential = 10 (Years/2.5)

Deterioration Factor Medium Potential = 10 (Years/5)

Deterioration Factor Low Potential = 10 (Years/10)

The Deterioration Factor for PRD damage is graphically demonstrated in the following figure.

Deterioration Factor.png

Adjustment for Redundant Relief Devices

If more than one valve is in place that protects the equipment and the valves are sized such that the failure of one valve to open does not reduce the relieving capacity below the required capacity then the calculated Deterioration Factor will be divided by 10 before determining the Probability Category.

Adjustment for Challenge Rate

Relief devices that are almost never challenged will have a very low probability of causing a loss of containment. Therefore, the probability of a relief device failure leading to a loss of containment  includes the likelihood of challenge or demand rate on that relief valve device.  The AllAssets Criticality Analysis provides two means of estimating the adjustment for the challenge rate for a relief device. 

One method is to estimate the likelihood of demand on a relief device, based on process knowledge or on operating experience.  This method is valid if the process has been in operation at least ten years.  If this is the case, use the following table to estimate the challenge rate and Adjustment Factor.

Estimated Challenge Rate

 Challenge Factor
More than once every 6 months 3
Once every 6 months to 2 years 1
Once every 2 to 5 years 0.7
Once every 5 to 10 years 0.5
Less than once every 10 years 0.3

An alternate method is using the ratio of operating pressure to Design Pressure for the equipment that the relief device is designed to protect.  Use the table below to determine the Challenge Factor.

Ratio of

operating/design pressure

 Challenge Factor
> 0.90 3
0.75 – 0.89 1
0.50 – 0.74 0.7
< 0.50 0.3

The Deterioration Factor is then adjusted by multiplying it by the Challenge Factor.

ESTABLISH THE PROBABILITY CATEGORY

The Probability Category is calculated as follows: 

Adjusted Deterioration Factor

 Probability Category
0-9 4
10-99 3
100-999 2
1000 + 1