API RP 581 - 3rd Ed.2016 - Add.2-2020 - Risk-Based Inspection Methodology

3-12 API RECOMMENDED PRACTICE 581
and may be preferred. One exception may be for two-phase piping systems. In this case, the upstream spill
inventory should be considered so that if a majority of the upstream material can be released as vapor, then a
vapor phase should be modeled. The results should be checked accordingly for conservatism. Items containing
two phases should have a closely approximated potential spill inventory to prevent overly conservative results.
The release rate equations are provided in the following sections. The initial phase within the equipment can
be determined using a fluid property solver that eliminates assumptions on the release rate calculations.
4.3.2 Liquid Release Rate Calculation
Discharges of liquids through a sharp-edged orifice is discussed in the work by Crowl and Louvar [1] and may
be calculated using Equation (3.3).
( )
A 2⋅gc ⋅ P
n
s
−Patm
n
=
d⋅ vn ,
⋅ρl⋅ (3.3)
C1
ρl
W C K
In Equation (3.3), the discharge coefficient, C , for fully turbulent liquid flow from sharp-edged orifices is in the
d
range of 0.60 ≤ ≤ 0.65 . A value of C = 0.61 is recommended [17] . Equation (3.3) is used for both flashing
C d
and non-flashing liquids.
d
The viscosity correction factor, K , can be determined from Figure 4.1 or approximated using Equation (3.4),
vn ,
both of which have been reprinted from API 520, Part 1. As a conservative assumption, a value of 1.0 may be
used.
K
⎛ 2.878 342.75 ⎞
= ⎜0.9935
+ + ⎟
⎝
⎠
vn , 0.5 1.5
Ren
Ren
−1.0
(3.4)
4.3.3 Vapor Release Rate Equations
There are two regimes for flow of gases or vapors through an orifice: sonic (or choked) for higher internal
pressures and subsonic flow for lower pressures [nominally, 103.4 kPa (15 psig) or less]. Therefore, vapor
release rates are calculated in a two-step process. In the first step, the flow regime is determined, and in the
second step the release rate is calculated using the equation for the specific flow regime. The transition
pressure at which the flow regime changes from sonic to subsonic is defined by Equation (3.5).
P
trans
⎛k
+ 1⎞
= Patm
⎜ ⎟
⎝ 2 ⎠
k
k −1
(3.5)
The two equations used to calculate vapor flow rate are shown below.
a) If the storage pressure, P
s
, within the equipment item is greater than the transition pressure, P
trans
,
calculated using Equation (3.5), then the release rate is calculated using Equation (3.6). This equation is
based on discharges of gases and vapors at sonic velocity through an orifice; see Crowl and Louvar [1] .
C ⎛
d
k ⋅MW ⋅g
⎞
c ⎛ 2 ⎞
Wn = ⋅An⋅Ps
⎜ ⎟⎜ ⎟
C2
⎝ RT ⋅
s ⎠⎝k+
1⎠
k + 1
k −1
(3.6)