Sizing of Gas Liquid Separators As explained in the previous lectures, the formula for calculating the settling velocity is: ut = 0.07[(L - v )/ )/v ]1/2 (10.10) Where
ut = settling velocity, m/s, L = liquid density, kg/m3, v = vapour density, kg/m3.
If a demister pad is not used, the value of ut obtained from equation (10.10) should be multiplied multiplied by a factor factor of 0.15 0.15 to provide provide a margin margin of safety and and to allow for flow surges.
Vertical
Gas Liquid Separators
Sizing Vertical Gas Liquid Separators The minimum allowable diameter will be given by: Dv =
(4Vv / us)
(10.11)
where Dv = minimum vessel diameter, m, Vv = gas, or vapour volumetric flow-rate, m3/s, us = superficial gas velocity, m/s us = ut, if a demister pad is used, and 0.15 ut for a separator without a demister pad; ut from equation (10.10), m/s. The height of the vessel outlet above the gas inlet should be sufficient to allow for disengagement of the liquid drops. A height equal to the diameter of the vessel or 1 m, which ever is the greatest, should be used, see Figure 10.51a. The liquid level will depend on the hold-up time necessary for smooth operation and control; typically 10 minutes would be allowed.
Example
± Sizing Vertical Gas Liquid Separators
Make a preliminary design for a separator to separate a mixture of steam and water; flow-rates: steam 2000 kg/h, water 1000 kg/h; operating pressure 4 bar. Solution
From steam tables, at 4 bar: saturation temperature 143.6°C, liquid density 926.4 kg/m3, vapour density 2.16 kg/m3. ut = 0.07[(926.4 - 2.16)/2.16]1/2 = 1.45 m/s (10.10) As the separation of condensate from steam is unlikely to be critical, a demister pad will not be specified So, ut = 0.15 * 1.45 = 0.218 m/s 2000 = 0.257 m3/s Vapour volumetric flow-rate = 3600*2.16 Dv =¥ [(4 * 0.257)/( * 0.218)] = 1.23 m, round to 1.25 m (4 ft) (10.11) 1000 Liquid volumetric flow-rate = ------------------- = 3.0 * 10 -4 m3/s 3600 * 926.14
Example
± Vertical Gas Liquid Separators- Contd
Allow a minimum of 10 minutes hold-up. Volume held in vessel = 3.0 * 10-4 * (10 * 60) = 0.18 m3 Volume
held-up Liquid depth required, hv = -------------------------vessel cross-sectional area 0.18 = --------------= 0.15 m ( *1.252/4) Increase to 0.3 m to allow space for positioning the level controller. What is the total height of the separator? And the L/D
Horizontal
Gas Liquid Separators
Sizing Horizontal Gas Liquid Separators In the design of a horizontal separator the vessel diameter cannot be determined independently of its length, unlike for a vertical separator. The diameter and length, and the liquid level, must be chosen to give sufficient vapour residence time for the liquid droplets to settle out, and for the required liquid hold-up time to be met. The most economical length to diameter ratio will depend on the operating pressure As a general guide the following values can be used:
Operating pressure, bar 0 - 20 20 - 35 >35
Length: diameter, Lv /Dv 3 4 5
The relationship between the area for vapour flow, Av , and the height above the liquid level, hv , can been found from tables giving the dimensions of the segments of circles; (see Perry and Green (1984), or from Figure 11.32 and 11.33 in Chapter 11.) For preliminary designs, set the liquid height at half the vessel diameter, hv = Dv /2 f v = 0.5, where f v is the fraction of the total cross-sectional area occupied by the vapour.
Partial Volume of Horizontal Vessels
Partial Volume of Horizontal Vessels
Example
± Sizing of Horizontal Gas Liquid Separator
Design a horizontal separator to separate 10,000 kg/h of liquid, density 962.0
kg/m3, from 12,500 kg/h of vapour, density 23.6 kg/m3. The vessel operating pr essur e will be 21 bar.
Solution
ut = 0.07[(962.0 - 23.6)/23.6]1/2 = 0.44 m/s Try a separator without a demister pad. ua = 0.15 * 0.44 = 0.066 m/s 12,500 -------------- = 0.147 m3/s Vapour volumetric flow-rate = 3600*23.6 Take hv = 0.5Dv and Lv /Dv = 4 Dv2 Cross-sectional area for vapour flow = -------- * 0.5 = 0.393 Dv2 4 0.147 Vapour velocity, uv = ------------ = 0.374 Dv-2 0.393Dv 2
Horizontal Separator Sizing (Contd.) Vapour residence time required for the droplets to settle to liquid surface = hv /ua = 0.5Dv /0.066 = 7.58Dv Actual residence time = vessel length/vapour velocity 4Dv = Lv /uv = ----------- = 10.70Dv3 0.374 Dv-2 For satisfactory separation required residence time = actual.
So,
7.58Dv = 10.70Dv3 Dv = 0.84 m, say 0.92 m (3 ft, standard pipe size)
Liquid hold-u p
time,
10,000 liquid volumetric flow-rate = --------------- = 0.00289 m3/s 3600*962.0 *0.922 liquid cross-sectional area = ----------- *0.5 = 0.332 m2 4
Horizontal
Separator Sizing (Contd.)
Length, Lv = 4 * 0.92 = 3.7 m Hold-up volume = 0.332 * 3.7 = 1.23 m3 Hold-up time = liquid volume/liquid flow-rate = 1.23/0.00289 = 426 s = 7 minutes. This is unsatisfactory, 10 minutes minimumrequired. Need to increase the liquid volume. This is best done by increasing the vessel diameter. If the liquid height is kept at half the vessel diameter, the diameter must be increased by a factor of roughly (10/7)0.5 = 1.2. New Dv = 0.92 * 1.2 = 1.1 m Check liquid residence time, *1.12 new liquid volume = ---------- *0.5*(4*1.1) = 2.09 m3 4 new residence time = 2.09/0.00289 = 723 s = 12 minutes, satisfactory
Horizontal Assume
Separator Sizing (Contd.)
that the level of liquid in the separator in the separator is 30%
From Table 10-64, the fraction of volume occupied by liquid is 0.25231* Therefore, vapour space volume is Vv = (1-0.25231) *V = 0.74769 * V V = (/4) * Dv2 * Lv = (/4) * Dv2 *4Dv = * Dv3
V
Cross sectional area for vapour flow = Vv/Lv =0.74769* *Dv3/4Dv = 0.74769*(/4)*Dv2 = 0.5869*Dv2 Vaour velocity = 0.147/(0.5869*D v2) = 0.2505 * Dv-2 Vapour residence time required to settle the liquid droplets to the surface = 0.7D v/).066 = 10.61*Dv Actual residence time = Vessel length/vapour veocity = 4Dv/0.2505*Dv-2 = 15.97 * Dv3 For satisfactory separation, settling time = actual residence time, i.e. 10.61D v = 15.96 Dv3 Therefore D = ¥(15.96/10.61) = 1.226 m, Length = 4D v = 4.904 m Hold up volume = 0.25231 * * Dv2/4 * 4Dv = 1.46 m3 Hold up time = 1.46/0.00289 = 505 Sec = 8.4 minutes ??? If a hold up time of 10 min. is required then the dia should be increased by a factor (10/8.4)0.5=1.09 Therefore the new D v = 1.226*1.09 = 1.338m = 4.38 ft round off to 4.5 ft New hold up time = 0.25231* /4 *(1.338)2 * (4*1.338)/.00289 = 656 Sec = 10.9 min
