Develop the relationship between height and volume of a hori

Develop the relationship between height and volume of a horizontal cylindrical separator (take diameter = d and length = L). What will be the volume of water at: d/3 from the bottom? = 2d/3 from the bottom ? and If the total volume of tank and its length are 2 Times 10^0 litre and 3.98 m respectively, calculate the mass of water when the tank is filled up to 5 m. Determine the diameter and seam-to-scam length of a horizontal separator for the following operating conditions. Determine the actual gas and oil capacity of the designed separator. Gas rate: 11803 scf/hr Gas specific gravity: 0.6 Oil rate: 13.28 m^3/h Oil gravity: 40 degree API Operating pressure: 6900 kPa Operating temperature: 15.6 degree C Droplet Size removal: 140 micron Retention time: 3 min. A vertical three-phase separator is half-full of liquid, determine its size for given the following data: Q_b = 33 m^3/hr SG_z = 0.6, Z = 0.99 Dropelt removal sizes are 100 microns for liquids, 500 microns for water and 200 microns for oil. Answer Problem 1 from textbook Chapter 16 (Vol 2, page 375).

Solution

>> Solution 2.1

As, Volume = Area*Length

As, Length = Height of cylinder upto which water is filled.

and, as Area = *d²/4

=> Volume, V = d²*h/4 .........REQUIRED RELATIONSHIP......

>> Now, at h = d/3

=> Volume, V = d²*d/12

=> Required Volume = d³/12

>> Now, at h = 2d/3

=> Volume, V = d²*2d/12

=> Required Volume = d³/6

>> Now, Total Volume, V = 2*10⁵ litre = 200 m³ , and,

Total Length of Cylinder, L= h = 3.98 m

=> *d²*h/4 = 200

Solving,

d = diameter of cylinder = 8.00 m

>> Now, at h = 5 m,

Volume filled, V = *d²*h/4 = *8²*5/4 = 251.256 m³

As, Density of Water = 1000 Kg/m³

As, Mass = Volume*Density

=> Mass = 251.256*1000 = 2.51*10⁵ Kg ......ANSWER.....