polykin.flow.prv

area_relief_liquid

area_relief_liquid(
    Q: float,
    P1: float,
    P2: float,
    mu: float,
    Gl: float,
    Kd: float = 0.65,
    Kw: float = 1.0,
    Kc: float = 1.0,
) -> float

Calculate the required effective discharge area of a pressure relief device in liquid service (single-phase flow).

The calculation is done according to the API standard 520, assuming the capacity of the valves is certified, as required by the ASME code.

References

• Sizing, Selection, and Installation of Pressure-relieaving Devices in Refineries: Part I—Sizing and Selection, API Standard 520, 10th ed., 2020.

PARAMETER	DESCRIPTION
Q	Required relieving volume flow rate (L/min). TYPE: float
P1	Upstream relieving pressure (bar). It can be absolute or gauge, as long as it is consistent with P2. TYPE: float
P2	Downstream back pressure (bar). It can be absolute or gauge, as long as it is consistent with P1. TYPE: float
mu	Viscosity at the relieving temperature (cP). TYPE: float
Gl	Relative density of the liquid at the relieving temperature with respect to water at standard conditions. TYPE: float
Kd	Effective discharge coefficient. Use Kd=0.65 when sizing a PRV and Kd=0.62 when sizing a rupture disk without PRV. TYPE: float DEFAULT: 0.65
Kw	Backpressure correction factor for balanced bellows valves. The value can be obtained from the manufacturer or estimated with the help of Figure 32 of the API standard 520. TYPE: float DEFAULT: 1.0
Kc	Combination correction factor for installations with a rupture disk upstream of the PRV. Use Kc=1.0 if there is no rupture disk, and Kc=0.9 if there is a rupture disk. TYPE: float DEFAULT: 1.0

RETURNS	DESCRIPTION
float	Effective discharge area (mm²).

Examples:

Estimate the required discharge area of a pressure relief valve in liquid service, according to the API standard 520. The required flow is 6814 L/min, the relieving pressure is 18.96 barg, the back pressure is 3.45 barg, the liquid relative density is 0.9, the liquid viscosity is 396 cP, and the valve back pressure correction factor is 0.97.

>>> from polykin.flow import area_relief_liquid
>>> A = area_relief_liquid(Q=6814, P1=18.96, P2=3.45, mu=396, Gl=0.9, Kw=0.97)
>>> print(f"Effective discharge area: {A:.0f} mm²")
Effective discharge area: 3172 mm²

Source code in src/polykin/flow/prv.py

def area_relief_liquid(Q: float,
                       P1: float,
                       P2: float,
                       mu: float,
                       Gl: float,
                       Kd: float = 0.65,
                       Kw: float = 1.0,
                       Kc: float = 1.0,
                       ) -> float:
    r"""Calculate the required effective discharge area of a pressure relief
    device in liquid service (single-phase flow). 

    The calculation is done according to the API standard 520, assuming the
    capacity of the valves is certified, as required by the ASME code.

    **References**

    * Sizing, Selection, and Installation of Pressure-relieaving Devices in
      Refineries: Part I—Sizing and Selection, API Standard 520, 10th ed., 2020.

    Parameters
    ----------
    Q : float
        Required relieving volume flow rate (L/min).
    P1 : float
        Upstream relieving pressure (bar). It can be absolute or gauge, as long
        as it is consistent with `P2`.
    P2 : float
        Downstream back pressure (bar). It can be absolute or gauge, as long as
        it is consistent with `P1`.
    mu : float
        Viscosity at the relieving temperature (cP).
    Gl : float
        Relative density of the liquid at the relieving temperature with respect 
        to water at standard conditions.
    Kd : float
        Effective discharge coefficient. Use `Kd=0.65` when sizing a PRV and
        `Kd=0.62` when sizing a rupture disk without PRV.
    Kw : float
        Backpressure correction factor for balanced bellows valves. The value
        can be obtained from the manufacturer or estimated with the help of 
        Figure 32 of the API standard 520.
    Kc : float
        Combination correction factor for installations with a rupture disk
        upstream of the PRV. Use `Kc=1.0` if there is no rupture disk, and
        `Kc=0.9` if there is a rupture disk.

    Returns
    -------
    float
        Effective discharge area (mm²).

    Examples
    --------
    Estimate the required discharge area of a pressure relief valve in liquid 
    service, according to the API standard 520. The required flow is 6814 L/min,
    the relieving pressure is 18.96 barg, the back pressure is 3.45 barg, the
    liquid relative density is 0.9, the liquid viscosity is 396 cP, and the valve
    back pressure correction factor is 0.97.
    >>> from polykin.flow import area_relief_liquid
    >>> A = area_relief_liquid(Q=6814, P1=18.96, P2=3.45, mu=396, Gl=0.9, Kw=0.97)
    >>> print(f"Effective discharge area: {A:.0f} mm²")
    Effective discharge area: 3172 mm²
    """

    # Convert pressures from bar to kPa
    P1 *= 1e2
    P2 *= 1e2

    A = 0.0
    A_old = 0.0
    converged = False
    MAX_ITER = 50
    for i in range(MAX_ITER):

        if i == 0:
            Kv = 1.0
        else:
            Re = 18800*Q*Gl/(mu*sqrt(A))
            Kv = 1/(0.9935 + 2.878/Re**0.5 + 342.75/Re**1.5)

        A = 11.78*Q/(Kd*Kw*Kc*Kv)*sqrt(Gl/(P1 - P2))

        if abs((A - A_old)/A) < 1e-5:
            converged = True
            break
        else:
            A_old = A

    if not converged:
        raise ValueError(f"Failed to converge after {MAX_ITER} iterations.")

    return A