Liquid-Vapor Separators (fluids.separator)

This module contains functionality for calculating rating and designing vapor-liquid separators.

For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker or contact the author at Caleb.Andrew.Bell@gmail.com.

Functions

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 [1]. This is a simplifying expression for terminal velocity and drag on particles.

vmax=KSBρl−ρgρgv_{max} = K_{SB} \sqrt{\frac{\rho_l-\rho_g}{\rho_g}}
Parameters
Kfloat

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

rholfloat

Density of liquid phase [kg/m^3]

rhogfloat

Density of gas phase [kg/m^3]

Returns
v_maxfloat

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.

vterm=vmax=4gdp(ρp−ρf)3CDρfvterm=(ρp−ρf)ρf4gdp3CDvterm=KSB4gdp3CDv_{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}}

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 [2]. For this reason using the drag coefficient expression directly is cleaner, but identical results can be found with the Sounders Brown equation.

References

1

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.

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 [1] to determine K as used in the following equation:

vmax=KSBρl−ρgρgv_{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:

mlmgρg/ρl=(1−x)xρg/ρl\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) [2], as follows:

KSB=exp⁡(−1.942936−0.814894X−0.179390X2−0.0123790X3+0.000386235X4+0.000259550X5)X=ln⁡[(1−x)xρg/ρl]K_{SB} = \exp(-1.942936 -0.814894X -0.179390 X^2 -0.0123790 X^3 + 0.000386235 X^4 + 0.000259550 X^5) X = \ln\left[\frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\right]

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

KSB=exp⁡(−1.877478097−0.81145804597X−0.1870744085X2−0.0145228667X3−0.00101148518X4)X=ln⁡[(1−x)xρg/ρl]K_{SB} = \exp(-1.877478097 -0.81145804597X -0.1870744085 X^2 -0.0145228667 X^3 -0.00101148518 X^4) X = \ln\left[\frac{(1-x)}{x}\sqrt{\rho_g/\rho_l}\right]
Parameters
xfloat

Quality of fluid entering separator, [-]

rholfloat

Density of liquid phase [kg/m^3]

rhogfloat

Density of gas phase [kg/m^3]

horizontalbool, optional

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

methodstr

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

Returns
Kfloat

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

1

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

2

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

3

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 [1] published in [2] and is widely used.

For 1 < P < 15 psia:

K=0.1821+0.0029P+0.0460ln⁡PK = 0.1821 + 0.0029P + 0.0460\ln P

For 15 <= P <= 40 psia:

K=0.35K = 0.35

For P < 5500 psia:

K=0.430−0.023ln⁡PK = 0.430 - 0.023\ln P

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

Parameters
Pfloat

Pressure of separator, [Pa]

horizontalbool, optional

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

Returns
Kfloat

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

2

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

1

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.

KSB=(ρp−ρf)ρf=4gdp3CDK_{SB} = \sqrt{\frac{(\rho_p-\rho_f)}{\rho_f}} = \sqrt{\frac{4 g d_p}{3 C_D}}
Parameters
Dfloat

Design diameter of the droplets, [m]

Cdfloat

Drag coefficient [-]

gfloat, optional

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

Returns
Kfloat

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('%.14f' %V)
0.76093307417658
0.56242939340131
0.50732895050696
0.48957142095508
0.48356021946899
0.48149076033622
0.48077414934614
0.48052549959141
0.48043916249756
0.48040917690193

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)
0.4803932186998

References

1

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