S. Avaji, ODCC Co., Tehran, Iran; Z. KHEZRI, PETROFORCE Co., Tehran, Iran; S. AVAJI, FALCON Co., Tehran, Iran; and Y. R. KHODAVERDILOU, ODCC Co., Tehran, Iran
Separators play a crucial role in separation processes, particularly in chemical engineering, and the sizing of this equipment is equally vital. Improper sizing can result in economic losses and create unfavorable process conditions.1 The separation process in this equipment relies on the differences in density among the various phases, and the design of the separator must promote efficient separation.2
In the oil and gas industry, various streams, including hydrocarbons, water and gas, are separated under specific temperature and pressure conditions. This separation process is primarily conducted using equipment such as slug catchers and separators. Separators, as fundamental pieces of process equipment, must be meticulously designed to ensure that downstream devices operate under optimal conditions.3 Process engineers recognize that determining the size of separators—particularly in three-phase flow situations—presents an intricate challenge due to the many variables that must be considered in the design.4
Separators can be configured either vertically or horizontally. Each design case should be evaluated individually; however, based on industrial usage and experience, vertical separators are recommended for applications such as compressor knockout (KO) drums, degassing boots, fuel gas KO drums, absorber feed KO drums and high-pressure production separators. Conversely, horizontal separators are typically used for reflux drums, three-phase separation and flare KO drums.5
The primary design principle of separators is the balance between gravitational and drag forces acting on the liquid droplet. According to gravitational theory, a liquid droplet can settle and separate from the accompanying phase when the net effect of gravitational and drag forces is directed downward and the force of gravity can overcome the drag force acting on a droplet.6 The two theories proposed for the sizing of separators are the droplet-settling theory and retention-time. The first theory is related to the balance of drag and gravity forces applied to the droplet. The second theory states that to reach the equilibrium of the liquid and gas phases inside the separator, the liquid must have a certain residence time. This time varies across various sizing projects and is contingent on the process.3 The application of software like computational fluid dynamics (CFD), in combination with neural networks and genetic algorithms for separator design, is progressing quickly. Nevertheless, there is a lack of studies that employ numerical solution techniques for sizing separators.7–11
Over the years, researchers have consistently sought to develop methods for sizing separators. Monnery and Svrcek were among the first to provide a comprehensive solution for sizing three-phase separators.12 Their method continues to be widely used by companies and process engineers. They outlined all necessary equations for sizing boot, weir and bucket-type separators, but it is important to note that their article lacks references regarding the accuracy of the equations and the final solution. Additionally, they did not compare their examples with real samples or experimental data, nor did they mention this issue. Boukadi, et al.,13 developed the method proposed by Stewart and Arnold,3 acknowledging that the changing specifications of the inlet flow to the separators over time may result in errors in sizing. This can lead to either over-design or under-design in the long term.
It was stated that fluid viscosity does not affect the relationships described by Stewart and Arnold; therefore, they introduced a new retention time that accounts for variations in viscosity over time. In their research, they utilized a diagram illustrating emulsion viscosity as a function of time. They identified the peak point on the diagram, which indicated the highest viscosity of the fluid within a specific time frame, as the viscosity of the fluid under investigation. Selecting this specific viscosity of the fluid resulted in a longer retention time and, consequently, a larger separator.13
Deng, et al.,14 introduced an equation to calculate the levels of light and heavy liquids by analyzing the flow dynamics in a three-phase separator equipped with a weir and bucket. Their equation is derived from the energy equation and incorporates the resistance of the bucket. The results of their study indicated that the height of the heavy liquid within the separator increases with an increase in flowrate and the ratio of heavy liquid density to light liquid density. Conversely, the liquid level decreases as the difference in height between the light and heavy liquids in the weir overflow increases. This indicates that the height disparity between the light and heavy liquids in weir overflows can serve as an adjustable input to regulate the liquid level. Using their proposed equation, the distinct levels of light and heavy liquids can be identified, allowing for the precise determination of the minimum length required to separate the phases, in comparison to laboratory findings.14
In their research, Igbagara, et al.,15 conducted a study on the sizing of a three-phase separator using the method developed by Monnery and Svrcek.12 This method was employed to determine the fundamental dimensions of the separator, including its diameter and length, as well as the various liquid levels within the separator (oil, water and gas). The sizing calculations in their study were computerized, and the results obtained exhibited a minimal margin of error when compared to actual data.15
This article seeks to define the concepts and principles of design for engineers by numerically solving various industrial and real-world examples related to the sizing of separators. Based on the results obtained and their comparison with the industrial data sheets provided by vendors, the numerical solution method presented in this article can serve as a reliable initial estimate. In this context, three examples of three-phase separators are presented: vertical separators, horizontal separators with weirs, and horizontal separators with boots.
VERTICAL THREE-PHASE SEPARATOR
FIG. 1 illustrates a vertical three-phase separator. All necessary data have been extracted from the actual project. The upcoming sections will detail the procedures/steps to manually calculate the dimensions of three-phase vertical separators (TABLE 1). Some input data, such as hold-up time, surge time, operating pressure and operating temperature, are subject to change, and the designer must determine them based on project conditions and criteria.
Step 1. Calculate or select the K value (ft/sec). Both the York16 and Gaussian process spatial alignment (GPSA) methods are utilized for this step, calculating K using each of the specified procedures. Ultimately, the minimum value obtained was chosen. This value may be specified by the owner and project process criteria and should be verified.
For 400 < P (Psi) < 5,500, the York relation16 is calculated using Eq. 1:
0.43 – 0.023 × lnP = 0.43 – 0.023 × ln(377) = 0.2935 (1)
and K from the GPSA design practice [0 < P (Psi) < 1,500] is calculated using Eq. 2:
0.35 – 0.0001 × (P – 100) = 0.35 – 0.0001 × (377 – 100) = 0.3223 --> selected K = 0.2935 (2)
Step 2. The calculation of vertical terminal velocity is next (Eq. 3). Terminal velocity is the highest speed that an object can reach while descending through a fluid.
Vt = K √[(ρL.L – ρv ) / ρv ] = 0.2935 × √[(40.578 – 1.81) / 1.81] = 1.36 (3)
Step 3. The vapor velocity is about 0.75–0.95 of the terminal velocity (Eq. 4).12
Vv = 0.75 × Vt = 0.75 × 1.36 = 1.02 (4)
Step 4. The vapor disengagement diameter is calculated using Eqs. 5 and 6:
Dvd = √[4Qv / (π × Vv )] = √[(4 × (72,607.02 / 3,600) / (π × 1.02)] = 5.02 (5)
Dvd = 5.02 × 12 = 60.24 (6)
Dvd must be rounded up to the nearest multiple of 6 in., so 63 in. (or 5.25 ft) is selected.
Dvd = 5.25
Step 5. The settling velocity of heavy liquid droplets in light liquid is calculated using Eq. 7:
VHL = [ks × (ρH.L – ρL.L)] / μL.L (7)
ks is Stokes’ law of the terminal velocity constant (in.cP.lb./min.ft3). This constant value is typically 0.163, except in cases where hydrocarbons are present as light liquids with a specific gravity (SG) of < 0.85 at 60°F and water or caustic is present as a heavy liquid. In this example, this constant of 0.163 will be maintained. Eq. 8 shows the numerical values for Eq. 7:
VHL = [0.163 × (65.86 – 40.578)] / 0.1 = 41.21 (8)
Step 6. The rising velocity of light liquid droplets in heavy liquid is calculated using Eq. 9:
VLH = [(ks × (ρH.L – ρL.L )) / μH.L ] = [(0.163 × (65.86 – 40.578)) / 1.8] = 2.29 (9)
Step 7. Calculation of the required time for heavy liquid droplets to settle through HL, which represents the length of the light liquid up to the nozzle. The minimum value for this distance is 1 ft—for this example, 1 ft is assumed. This value should be verified against project criteria (Eq. 10).
HL = 1
tH.L – res = (12HL / VHL ) = [(12 × 1) / 41.21] = 0.29 (10)
Step 7. The calculation of the required time for settling light liquid droplets through HH , which is the height from the bottom of the bottom tangent line (T.L) up to the heavy liquid interface (holdup for heavy liquid). The minimum value for this height is typically set at 1 ft; however, in this example, it is fixed at 2 ft. This value may vary based on project criteria, and process engineers should be mindful of this adjustment (Eq. 11).
HH = 2
tL.L – res = (12HH / VLH ) = [(12 × 2) / 2.29] = 10.48 (11)
Step 8. The calculations related to the baffle plate. If a baffle plate is present in the separator, the area of the baffle plate must be calculated to determine the area occupied by heavy and light liquids in each phase.13–16 Subsequently, the residence time for each phase will be calculated (Eq. 12) and compared with the previously calculated residence time for each phase (FIG. 2).
∆ρ = ρL.L + ρv = 40.578 – 1.81 = 38.76 (12)
HR indicates the height of light liquid above the holdup height. Assume a height of 1 ft or 12 in. This value will be checked by the selected holdup time (TH = 15 min) (Eq. 13).
HR + HL = 1 + 1 = 2 ft = 24
AD = 7.48 × [(QH.L + QL.L ) / G] (13)
G represents the volume of liquid that can be loaded onto the baffle, considering the density difference, as illustrated in FIG. 3 and Eq. 14. The numerical values have been inserted here into Eq. 14:
G = 9,800
AD = 7.48 × [(38.85 + 155.385) / 9,800] = 0.148 (14)
Step 9. In this step, we will recalculate the value using WD and compare the two calculated amounts, selecting the larger one. For this purpose, assume WD is 4 in. (this value should also be verified against the separator vendor), and calculate AD using Eqs. 15 and 16 and TABLE 2.
It can be seen from FIG. 2 that AL = At – AD = 21.64 – 0.577 = 21.07 ft2. The new residence time for heavy and light liquids can be calculated using Eqs. 17 and 18:
Now, τL.L–res and τH.L–res should be compared to tL.L–res and tH.L–res, respectively. If these values exceed τL.L–res and τH.L–res, the calculations are correct; otherwise, the diameter should be increased. In this example, the condition is met. Additionally, HR must be compared to the previously selected HR (Eq. 19).
It is evident that HR.new is greater than the old value; therefore, rounding up HR.new has been chosen as the final value (HR.new = 2 ft).
Step 10. The next step is to calculate the height of the liquid under surge conditions. Surge conditions refer to the scenario in which the height of the liquid rises from the normal liquid level (NLL) to the high liquid level (HLL) (Eq. 20).
Round up the Hs to the nearest integer value (Hs = 2 ft).
Step 11. The calculation of the total liquid volume fraction, the density of the liquid mixtures, the density of the entire mixture (including liquid, liquid-vapor) and the total volumetric flowrate are calculated using Eqs. 21–24, respectively.
Step 12. The nozzle diameter can be calculated using Eq. 25:
Round up dN to 10 in.
dN = 10 in.
The vapor disengagement height can be calculated as 0.5D; however, the presence of a mist eliminator should be carefully studied. If there is a mist eliminator, Eq. 26 is used.
HD = max [0.5D & ((24 + 0.5dN ) / 12)] (26)
Without a mist eliminator, Eq. 27 is used.
HD = max [0.5D & ((36 + 0.5dN ) / 12)] (27)
In this example, a mist eliminator is considered (Eq. 28).
HD = max [0.5 × 5.25 & ((24 + 0.5 × 10) / 12)] = max (2.625 & 2.417) = 2.625 (28)
HBN refers to the height of the liquid measured from the top of the baffle to the feed nozzle (Eq. 29).
HBN = 0.5 × dN + max(2 & (Hs + 0.5)) = 0.5 × 0.77 + max(2 & (2 + 0.5)) = 2.88 (29)
Round up HBN to 3 ft.
The minimum height of the liquid on the baffle plate is typically considered to be 0.5 ft. The thickness of the mist eliminator (Hmist ) is at least 0.5 ft, and the height between the top of the tangent line (TL ) and the mist eliminator (HU ) has a minimum value of 1 ft (Eq. 30).
HA = 0.5 & Hmist = 0.5 & HU = 1 (30)
The calculation has been completed, and the final result is reported in Eq. 31.
HT = HA + HBN + Hmist + HU + HD + HS + HR + HL + HL (31)
HT = 0.5 + 3 + 0.5 + 1 + 2.625 + 2 + 2 + 1 + 2 = 14.63 ft = 14.63 × 0.3048 = 4.46 m
D = 5.25 ft = 5.25 × 0.3048 = 1.6 m
Additionally, HT / D should be monitored and must fall within the range of 1.5 to 6 (Eq. 32).
(HT / D) = (14.63 / 5.25) = 2.78 (32)
HORIZONTAL THREE-PHASE SEPARATOR (WITH WEIR)
FIG. 4 is a diagram of a real three-phase separator. The specifications for any outlet stream are demonstrated here. The diameter and length of this separator will be calculated numerically, without relying on computers, to enhance understanding. This example serves as a useful guide for initial calculations; however, sizing must be checked case by case and may vary depending on project criteria (TABLE 3). For instance, residence time is a crucial parameter that must be discussed and specified by the client. In this example, a residence time of 5 min is assumed. Additionally, a particle diameter of 150 microns is selected for this vessel sizing, which may differ in other projects.
Step 1. Calculate the C(Re)2 and drag coefficient from FIG. 5 (Eq. 33).
Step 2. Calculate the settling velocity using Eq. 34:
Step 3. Standard length-to-diameter (L/D) ratios for horizontal separators generally range from 2.5–6. A significant liquid surge volume is needed to achieve a longer retention time, which facilitates a more thorough release of dissolved gas and, if needed, provides surge volume for the circulation system (Eq. 35).
L/D = 3.3 (35)
Step 4. The velocity coefficient is typically regarded as ranging from 0.5 to 0.6. In this instance, 0.6 is used for this parameter; however, a designer has the option to modify and choose different values for their project.
F = 0.6
Step 5. The required vapor velocity is calculated using Eq. 36:
Vm = F × (L / D) × Vs = 0.6 × 3.3 × 0.197 = 0.39 (36)
Step 6. The light liquid velocity in heavy liquid is calculated using Eq. 37:
Based on the total design criteria, the maximum value of UL,L is 250 mm/min; therefore, UL.L/H.L = 250 is selected for this velocity.
Step 7. The heavy liquid velocity in light liquid is calculated using Eq. 38:
Step 8. The required vapor cross sectional area is calculated using Eq. 39:
Step 9. The liquid height (HLL) to vessel diameter, which is shown as h1 / D, should be specified. The value of 0.7 is recommended for this height and is selected for this purpose (Eq. 40).
h1 / D = 0.7 (40)
Step 10. Calculate the ratio of the surface area occupied by liquids to the total surface area of the separator by using Eq. 41:17
Step 11. Calculate the ratio of the surface area occupied by vapor to the total surface using Eq. 42:
Av / AT = 1 – (Al / AT ) = 1 – 0.75 = 0.25 (42)
Step 12. Calculate the total area using Eq. 43:
Av / AT = 0.25 --> AT = Av / 0.25 = 0.09 / 0.25 = 0.36 (43)
Step 13. Calculate the liquid area using Eq. 44:
Al / AT = 0.75 --> Al = 0.75 × 0.36 = 0.27 (44)
Step 14. Calculate the total vessel diameter using Eq. 45:
D = √4AT / π = √(4 × 0.36) / π = 0.6807 m = 680.07 (45)
Step 15. According to the calculated value for the diameter, a rounded-up value is selected. The next appropriate choice for the diameter of the separator is 800 mm. Although 700 mm was initially considered, it was excluded to simplify the calculations. However, the reader is encouraged to perform the calculations using the 700 mm value if desired.
D = 800
Step 16. The flow path length is calculated using Eq. 46:
L/D = 3.3 --> L = 3.3 × 800 = 2,640 (46)
Step 17. The TL – TL length is calculated using Eq. 47:
L’ = L + 25.4 × (1.5 × (d1 + d2 )) = 2,640 + 25.4 × (1.5 × (4 + 4)) = 2,944.8 (47)
Step 18. The high liquid level (h1 = HLL) is calculated using Eq. 48:
h1 / D = HLL / D = 0.7 --> h1 = HLL = 0.7 × 800 = 560 (48)
Step 19. The volume of the HLL is calculated using Eq. 49:17
Step 20. Select the low liquid level (h2 = LLL). This value should be specified by the owner or project criteria (Eq. 50).
h2 = LLL = 700 mm (50)
Step 21. The volume of the LLL is calculated using Eq. 51:
Step 22. Calculate the surge volume using Eq. 52:
Vsurge = VHLL – VLLL = 1.1 – 1.37 = –0.27 (52)
Due to the surge volume being negative, the diameter must be increased.
Step 23. Select the new diameter and repeat Steps 16 to 22.
Dnew = 1,550L = 5,115 mm l’ = 5,419.8 mm ≈ 5,500 mm h1 = 1,085 mm VHLL = 7.65 m3 h2 = 700 mm VLLL = 4.48 m3 Vsurge = 3.16 m3
Step 24. Calculate the residence time of light liquid. The calculated residence time must be ≤ to the residence time selected (5 min) (Eq. 53).
Step 25. Calculate the NLL (hN.L) and liquid volume at NLL using Eqs. 54 and 55:
At this time, the heavy liquid falling and light liquid rising should be checked. Calculations are first performed for the heavy liquid phase.
Heavy liquid calculation (falling)
Step 26. Calculate the baffle (weir) space using Eq. 56:
B = (2 / 3)l’ = (2 / 3) × 5,419 = 3,613.2 (56)
Step 27. 3,700 mm is chosen as the first trial for baffle space height (Eq. 57).
B = 3,700 (57)
Step 28. The total liquid volumetric flowrate can be calculated using Eq. 58:
Qt = QH.L + QL.L = [mH.L / (60 × ρH.L )] + [mL.L / (60 × ρL.L )] = [9,955 / (60 × 988)] + [31,000 / (60 × 728.4)] = 0.88 (58)
Step 29. Calculate the high liquid level area using Eq. 59:
AHLL = (VHLL / l’ ) = [7.65 / (5,419 × 10–3)] = 1.41 (59)
Step 30. Calculate the horizontal velocity at the HLL area using Eq. 60:
UhHLL = 1,000 × (Qt / AHLL ) = [(1,000 × 0.88) / 1.41] = 621.8 (60)
Step 31. Calculate the required vertical distance from HLL for suitable settling using Eq. 61:
ZHLL = [(B(from step 2) × UH.L / L.L) / UhHLL ] = [(3,700 × 250) / 621.8] = 1,487.6 (61)
Step 32. Calculate the HLL (or h1 ) – ZHLL height. This value should be negative until liquid droplets can reach the bottom of the vessel. If the value is positive, L/D or HLL/D must be changed (Eq. 62).
h1 – ZHLL = 1,085 – 1,487.6 = –402.6 (62)
Step 33. Calculate the LLL area using Eq. 63:
ALLL = VLLL / l’ = [4.48 / (5,419 × 10–3)] = 0.83 (63)
Step 34. Calculate the horizontal velocity at the LLL area (Eq. 64).
UhHLL = 1,000 × (Qt / ALLL ) = [(1,000 × 0.88) / 0.83] = 1,060.26 (64)
Step 35. Calculate the required vertical distance from LLL for suitable settling (Eq. 65).
ZLLL = [(B(from step 2) × UH.L / L.L ) / UhLLL ] = [(3,700 × 250) / 1,060.26] = 872.43 (65)
Step 36. Calculate the LLL (or h2) – ZHLL (Eq. 66).
h2 – ZLLL = 700 – 872.43 = –172.43 (66)
Step 37. Select the baffle height (h3) and HLL for heavy liquid (h4) (HIL); 75 mm lower is the suggested value for both heights (Eqs. 67 and 68).
h3 = h2 – 75 = 700 – 75 = 625 (67)
h4 = h3 – 75 = 625 – 75 = 550 (68)
Light liquid calculation (rising)
Step 38. Calculate the vertical rise within the baffle space distance (Eq. 69).
ZVert = [(B(from step 2) × UH.L / L.L ) / UhHLL ] = [(3,700 × 250) / 1,060.26] = 872.43 (69)
Step 39. Calculate the h4 – ZVert height (Eq. 70).
h4 – ZVert = 550 – 872.43 = –322.43 (70)
Step 40. Select the LLL of the heavy liquid (LIL = h5 ). The minimum recommended value for LLL is 300 mm; however, it may vary across different projects, and the designer must follow the project criteria.
h5 = LIL = 300
Step 41. Select the vortex breaker height (h6). A common value for this height is 100 mm, and this value is considered in this example.
h6 = 100
Step 42. Calculate the NLL for heavy liquid (hNIL). It is assumed that the height of hNIL falls between the heights of h4 and h5 (Eq. 71).
hNIL = [(h4 + h5 ) / 2] = [(550 + 300) / 2] = 425 (71)
Step 43. Calculate the heavy liquid volume at HIL (Eq. 72).
Step 44. Calculate the heavy liquid volume at LIL (Eq. 73).
Step 45. Calculate the heavy liquid volume at NIL (Eq. 74).
Step 46. Calculate the heavy liquid volume at h6 up to the baffle (Eq. 75).
Step 47. Calculate the surge volume for heavy liquid (Eq. 76).
VSur/H = VHIL – VLIL = 2.22 – 0.95 = 1.27 (76)
Step 48. Calculate the surge time for heavy liquid (Eq. 77).
Step 49. Calculate the residence time for heavy liquid (Eq. 78).
Step 50. Calculate the heavy liquid holding time. The minimum acceptable value is 4 min–5 min, and this limitation must be checked vs. project criteria (Eq. 79).
tholding / H = tSur/H + tRes/H = 7.56 + 8.12 = 15.68 (79)
Step 51. Calculate the light liquid volume at NLL up to the vessel (Eq. 80).
VNLL = [(ANLL (refer to step 25 – section 1) × B ) / 1,000] = [(1.12 × 3,700) / 1,000] = 4.16 (80)
Step 52. Calculate the light liquid residence time (Eq. 81).
The residence time must be ≥ to the selected residence time of 5 min. Therefore, the selected baffle distance (B) must be increased. Through trial and error, the minimum selected baffle distance is determined to be 5,200 mm. Additionally, it should be less than (l’ ) from Step 23. Due to 3.7 min. being < 5 min., all calculations must be repeated from Step 28, and 1,000 mm should be selected for LLL or h2.
Bnew = 5000 mm
Finally, tRes/L = 4.97 ≈ 5 min and the calculated dimensions are summarized in TABLE 4 and FIG. 6.
Part 2 of this article will appear in the July issue. HP
LITERATURE CITED
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Sina Avaji serves as a Process Engineer in the Process department at Oil Design and Construction Co. (ODCC) located in Tehran, Iran. Before that, he spent approximately 3 yr at Sazeh Co. Previously, Avaji served as Technical Director at the Shiraz University Laboratory for 2 yr. The author can be reached at sinaavaji@gmail.com.
Zahra Khezri has been a Process Engineer in the Process department at Petroforce Co. for 2 yr. Khezri is a graduate of the University of Tehran with an MS degree in chemical engineering.
Saeed Avaji is a Process Engineer in the Process department at Falcon Co. He has been with Falcon Co. for 5 yr. Saeed is a graduate of the Shiraz University of Technology.
Yaser Rasti Khodaverdilou has 2 yr of professional experience as a Process Engineer within the Process department at Oil Design and Construction Company (ODCC). Prior to this role, he accumulated 2 yr of experience at Oil Industries Commissioning and Operation Company (OICO), and an additional 2 yr at Hampa Engineering Corp. Khodaverdilou is engaged in doctoral studies in chemical engineering at Shiraz University, where he is in the final stages of defending his doctoral thesis.