Hydrocarbon Processing - August 2021 - 35

Valves, Pumps and Turbomachinery
valve was sized using a two-point Omega method, resulting in
the maximum mass flux and required area of 36,890 kg/(s - m2
, respectively.
)
and 134.5 mm2
To size the PSV using the proposed method, the subcooled
propane at the relief condition was flashed using an isentropic
path (through an expander with 100% efficiency in the simulatora
environment).
At the first stage, the pressure was decreased
to find the boiling point (Psat
subcooled set between Pr
and Psat
= 722.2 kPaa). Two sets of data (a
and a flashed set between Psat
and Pb) were then generated and are presented in TABLE 2. The
subcooled set was fitted to a second-order polynomial, whereas
the flashed set was fitted by two functions, a seconded-order
polynomial and an exponential function. At the final stage, the
maximum mass fluxes were added and the required area was calculated.
The results are also summarized in TABLE 2. Both polynomial
and exponential functions show almost the same results.
Eq. 23 can be used to evaluate the subcooled mass flux using
an average density of 509.28 kg/m3
kg2/(s2
to be Gs
- m4), showing the same result.
Note: If the relief pressure is at or very close to (slightly subcooled
liquid) the saturation pressure, then it is recommended
that the subcooled regime be ignored and the PSV be sized in
one step using Eq. 1. For such a condition, the flashed data starting
from the saturation point are fitted by an exponential function,
but the relief pressure should be used for Eqs. 21 and 22.
Simpson9
provided an example to size a rupture disk for relieving
181,437 kg/hr of 703.3 kPaa condensate saturated at 689.5
2 = 1,370,914,531
Takeaway. To avoid numerous calculation steps of the numerical
solution of Eq. 1 to size pressure relief valves, an analytical
approach is derived to solve an integral part of the homogeneous
direct-integration method by fitting three density-pressure data
points to a linear, a second-order polynomial or an exponential
equation (more data points, up to six, are recommended to evaluate
density-pressure trend and relationship). The approach is
straightforward, targeting the throat pressure, calculating the
mass flux, and then sizing the PSV.
kPaa. The discharge coefficient and the total backpressure were
assumed to be 0.62 and atmospheric pressure, respectively. Using
the two-point model prediction and the numerical solution
of Eq. 1, the throat pressure, the maximum mass flux and the
required area were calculated to be 688.8 kPaa, 5,136.3 kg/(s2
- m4
) and 15,806 mm2
, respectively. Three data points at 689.5,
668.8 and 655.0 kPaa were selected and fitted to an exponential
function, leading to Eq. 25:
ρ = 1.4692 × 10-4e0.02265P
R2
= 0.9928
(25)
Using the relief pressure of 703.3 kPaa, the throat pressure,
the maximum mass flux, and the required area can be calculated
using Eqs. 22, 21 and 2, respectively, as:
Pt
= 672.7 kPaa
G = 5,181.3 kg/(s - m2
A = 15,690 mm2
)
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Hydrocarbon Processing | AUGUST 2021 35
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