Liquid-Vapor Separators (fluids.separator)¶
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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
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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
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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
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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