Liquid-Vapor Separators (fluids.separator)

fluids.separator.v_Sounders_Brown(K, rhol, rhog)[source]

Calculates the maximum allowable vapor velocity in a two-phase separator to permit separation between entrained droplets and the gas using an empirical K factor, named after Sounders and Brown [R742]. This is a simplifying expression for terminal velocity and drag on particles.

\[v_{max} = K_{SB} \sqrt{\frac{\rho_l-\rho_g}{\rho_g}}\]
Parameters

K : float

Sounders Brown K factor for two-phase separator design, [m/s]

rhol : float

Density of liquid phase [kg/m^3]

rhog : float

Density of gas phase [kg/m^3]

Returns

v_max : float

Maximum allowable vapor velocity in a two-phase separator to permit separation between entrained droplets and the gas, [m/s]

Notes

The Sounders Brown K factor is related to the terminal velocity as shown in the following expression.

\[ \begin{align}\begin{aligned}v_{term} = v_{max} = \sqrt{\frac{4 g d_p (\rho_p-\rho_f)}{3 C_D \rho_f }}\\v_{term} = \sqrt{\frac{(\rho_p-\rho_f)}{\rho_f}} \sqrt{\frac{4 g d_p}{3 C_D}}\\v_{term} = K_{SB} \sqrt{\frac{4 g d_p}{3 C_D}}\end{aligned}\end{align} \]

Note this form corresponds to the Newton’s law range (Re > 500), but in reality droplets are normally in the intermediate or Stoke’s law region [R743]. For this reason using the drag coefficient expression directly is cleaner, but identical results can be found with the Sounders Brown equation.

References

R742(1,2)

Souders, Mott., and George Granger. Brown. “Design of Fractionating Columns I. Entrainment and Capacity.” Industrial & Engineering Chemistry 26, no. 1 (January 1, 1934): 98-103. https://doi.org/10.1021/ie50289a025.

R743(1,2)

Vasude, Gael D. Ulrich and Palligarnai T. Chemical Engineering Process Design and Economics : A Practical Guide. 2nd edition. Durham, N.H: Process Publishing, 2004.

Examples

>>> v_Sounders_Brown(K=0.08, rhol=985.4, rhog=1.3)
2.2010906387516167
fluids.separator.K_separator_Watkins(x, rhol, rhog, horizontal=False, method='spline')[source]

Calculates the Sounders-Brown K factor as used in determining maximum allowable gas velocity in a two-phase separator in either a horizontal or vertical orientation. This function approximates a graph published in [R744] to determine K as used in the following equation:

\[v_{max} = K_{SB}\sqrt{\frac{\rho_l-\rho_g}{\rho_g}}\]

The graph has K_{SB} on its y-axis, and the following as its x-axis:

\[\frac{m_l}{m_g}\sqrt{\rho_g/\rho_l} = \frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\]

Cubic spline interpolation is the default method of retrieving a value from the graph, which was digitized with Engauge-Digitizer.

Also supported are two published curve fits to the graph. The first is that of Blackwell (1984) [R745], as follows:

\[ \begin{align}\begin{aligned}K_{SB} = \exp(-1.942936 -0.814894X -0.179390 X^2 -0.0123790 X^3 + 0.000386235 X^4 + 0.000259550 X^5)\\X = \log\left[\frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\right]\end{aligned}\end{align} \]

The second is that of Branan (1999), as follows:

\[ \begin{align}\begin{aligned}K_{SB} = \exp(-1.877478097 -0.81145804597X -0.1870744085 X^2 -0.0145228667 X^3 -0.00101148518 X^4)\\X = \log\left[\frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\right]\end{aligned}\end{align} \]
Parameters

x : float

Quality of fluid entering separator, [-]

rhol : float

Density of liquid phase [kg/m^3]

rhog : float

Density of gas phase [kg/m^3]

horizontal : bool, optional

Whether to use the vertical or horizontal value; horizontal is 1.25 higher

method : str

One of ‘spline, ‘blackwell’, or ‘branan’

Returns

K : float

Sounders Brown horizontal or vertical K factor for two-phase separator design only, [m/s]

Notes

Both the ‘branan’ and ‘blackwell’ models are used frequently. However, the spline is much more accurate.

No limits checking is enforced. However, the x-axis spans only 0.006 to 5.4, and the function should not be used outside those limits.

References

R744(1,2)

Watkins (1967). Sizing Separators and Accumulators, Hydrocarbon Processing, November 1967.

R745(1,2)

Blackwell, W. Wayne. Chemical Process Design on a Programmable Calculator. New York: Mcgraw-Hill, 1984.

R746

Branan, Carl R. Pocket Guide to Chemical Engineering. 1st edition. Houston, Tex: Gulf Professional Publishing, 1999.

Examples

>>> K_separator_Watkins(0.88, 985.4, 1.3, horizontal=True)
0.07951613600476297
fluids.separator.K_separator_demister_York(P, horizontal=False)[source]

Calculates the Sounders Brown K factor as used in determining maximum permissible gas velocity in a two-phase separator in either a horizontal or vertical orientation, with a demister. This function is a curve fit to [R747] published in [R748] and is widely used.

For 1 < P < 15 psia:

\[K = 0.1821 + 0.0029P + 0.0460\ln P\]

For 15 <= P <= 40 psia:

\[K = 0.35\]

For P < 5500 psia:

\[K = 0.430 - 0.023\ln P\]

In the above equations, P is in units of psia.

Parameters

P : float

Pressure of separator, [Pa]

horizontal : bool, optional

Whether to use the vertical or horizontal value; horizontal is 1.25 times higher, [-]

Returns

K : float

Sounders Brown Horizontal or vertical K factor for two-phase separator design with a demister, [m/s]

Notes

If the input pressure is under 1 psia, 1 psia is used. If the input pressure is over 5500 psia, 5500 psia is used.

References

R748(1,2)

Otto H. York Company, “Mist Elimination in Gas Treatment Plants and Refineries,” Engineering, Parsippany, NJ.

R747(1,2)

Svrcek, W. Y., and W. D. Monnery. “Design Two-Phase Separators within the Right Limits” Chemical Engineering Progress, (October 1, 1993): 53-60.

Examples

>>> K_separator_demister_York(975*psi)
0.08281536035331669
fluids.separator.K_Sounders_Brown_theoretical(D, Cd, g=9.80665)[source]

Converts a known drag coefficient into a Sounders-Brown K factor for two-phase separator design. This factor is the traditional way for separator diameters to be obtained although it is unnecessary and the theoretical drag coefficient method can be used instead.

\[K_{SB} = \sqrt{\frac{(\rho_p-\rho_f)}{\rho_f}} = \sqrt{\frac{4 g d_p}{3 C_D}}\]
Parameters

D : float

Design diameter of the droplets, [m]

Cd : float

Drag coefficient [-]

g : float, optional

Acceleration due to gravity, [m/s^2]

Returns

K : float

Sounders Brown K factor for two-phase separator design, [m/s]

Notes

Drag coefficient is a function of velocity; so iteration is needed to obtain the most correct answer. The following example shows the use of iteration to obtain the final velocity:

>>> from fluids import *
>>> V = 2.0 
>>> D = 150E-6
>>> rho = 1.3
>>> rhol = 700.
>>> mu = 1E-5
>>> for i in range(10):
...     Re = Reynolds(V=V, rho=rho, mu=mu, D=D)
...     Cd = drag_sphere(Re)
...     K = K_Sounders_Brown_theoretical(D=D, Cd=Cd)
...     V = v_Sounders_Brown(K, rhol=rhol, rhog=rho)
...     print(V)
0.760933074177
0.562429393401
0.507328950507
0.489571420955
0.483560219469
0.481490760336
0.480774149346
0.480525499591
0.480439162498
0.480409176902

The use of Sounders-Brown constants can be replaced as follows (the v_terminal method includes its own solver for terminal velocity):

>>> from fluids.drag import v_terminal
>>> v_terminal(D=D, rhop=rhol, rho=rho, mu=mu)
0.4803932186998833

References

R749

Svrcek, W. Y., and W. D. Monnery. “Design Two-Phase Separators within the Right Limits” Chemical Engineering Progress, (October 1, 1993): 53-60.

Examples

>>> K_Sounders_Brown_theoretical(D=150E-6, Cd=0.5)
0.06263114241333939