Multiphase CFD Simulation of Flow Inside Liquid Seal Drums of the

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Multiphase CFD Simulation of Flow Inside Liquid Seal Drums of the Refinery Flare System Randheer Yadav, Amitkumar Parekh, Ajay Gupta, and Asit Kumar Das* Reliance Technology Group (RTG), MAB, RTG Block, B3-G, Reliance Industries Limited, Jamnagar Refinery, Motikhavadi, Digvijayagram, Jamnagar, Gujarat-361140, India ABSTRACT: The present work deals with improving the reliability of the liquid seal drum in the refinery flare system. CFD (based on volume of fluid concept) as well as theoretical modeling have been used for deciphering the hydrodynamics in two different designs (designated as design-1 and design-2) of the liquid seal drums. Results of the CFD simulations showed that the internals present in design-1 facilitate in bubble coalescing, thus resulting in large sized Taylor bubbles, which cause large fluctuations in the liquid level. Large level fluctuations create problems such as flare puffing, knocking, and dislodging of seal drum internals. On the basis of the CFD model findings, a one-dimensional model based on Taylor bubble phenomenon1 has been adopted. Subsequently, the 1D model was used for calculating the Taylor bubble size and liquid level fluctuations. The 1D model was also used to predict the bubble size and liquid level fluctuation in another design (design-2) of the seal drum. Design-2 was also tested using CFD, which shows smooth passage of flare gas in the form of small bubbles with little fluctuation in liquid level. On the basis of the study, it was suggested to change the design-1 by design-2. Suggestions were implemented in the plant, which relieved it of problems faced with design-1. This led to reliability improvement and substantial monetary benefits.

1. INTRODUCTION 1.1. Seal Drum Location and Application in Refinery. A flare system is a critical component for refinery process safety management. The primary function of a flare is to use combustion to convert flammable, toxic, or corrosive vapors to less objectionable compounds. All processes and storage units in the refinery are connected to the flare system. This is required for safe and quick disposal of the hydrocarbons, both in normal running operation of the unit as well as under any abnormalities. Figure 1 shows the components of a typical flare system. As shown in Figure 1, the gases from the process/storage units pass through the knock out drum (KOD) to knock out the liquid drops that are usually present in the process vapors. Removal of the liquid drops helps in efficient burning of the hydrocarbon vapors in the flare stacks. One or more KODs may be used for this purpose depending on the volume of the flare off gases. After exiting from the KOD, the flare gases pass through the liquid seal drums (LSD). In the liquid seal drum, adequate water seal (Figure 2) is provided so as to stop the ingress of the atmospheric air into the upstream units. The flare gases exiting from the liquid seal drum go to the flare stack. 1.2. Previous Work. As a seal drum is an important part of the refinery flare system, there have been a number of fundamental as well as application oriented studies about it. Richards and Terrell2 discuss the advantages of baffle in the liquid seal drum. Michelson and Levy3 obtained a patent for their arrangement for minimizing flow pulsing in flare seal drums. Seebold4 suggested that the periodic surges of flame that occasionally burst forth from elevated flares into the quietude of the nighttime sky are often caused by seal drum sloshing. Ibrahim5 has discussed in detail the dynamics of liquid sloshing and effect of container geometry on liquid motion. The above references and literature cited r 2011 American Chemical Society

Figure 1. Components of a flare system.

therein provide an overview of the functions and design considerations of the seal drums. However, the effect of seal drum hydrodynamics on its performance has not been dealt with in detail. Design of the liquid seal drum has not been well understood. This is primarily due to the following reasons. (1) It is difficult to account for the complex two-phase flow phenomena in the liquid seal drums, for example, water sloshing and level fluctuations due to bubble movements. (2) Turbulence in LSD is a function of flare gas load, which is a highly fluctuating parameter. Modeling turbulence in itself is a challenging task. (3) Enough computational power was not available in the past to solve the three-dimensional NavierStokes equations. Received: September 15, 2011 Accepted: December 1, 2011 Published: December 01, 2011 1073

dx.doi.org/10.1021/ie202683h | Ind. Eng. Chem. Res. 2012, 51, 1073–1082

Industrial & Engineering Chemistry Research

Figure 2. Schematic representations of gas flow in a liquid seal drum (design-1).

(4) Full scale testing of new designs is economically unviable. New designs that look promising at the pilot scale may give unforeseen problems when scaled and put in the operation. Vendor guidelines being proprietary are not available in open literature. The guidelines available in open literature6,7 are for the flare system as a whole, and they do not treat liquid seal drum in detail. They give general recommendations and suggest for contacting the vendor for specific issues with the equipments. Parry8 has summarized the general recommendations of the American Petroleum Institute (API) on liquid seal height and seal drum internal design. 1.3. Operating Issues with Seal Drums. The seal drum appears simple but can cause significant worry to refinery engineers if not designed and operated properly. Operating issues such as flare puffing and knocking, sloshing, and dislodging of internals may be observed with ill-designed seal drums. Flare puffing and knocking is a prevalent issue with seal drums. Flare puffing is a sudden release of fire ball from the flare stack followed by a quiescent period. This phenomenon is continually repeated. Flare puffing creates a noise at the flare stack, which is termed as knocking. Flare puffing and knocking are linked to the size of the bubble formed when flare gas passes through the liquid pool. The bubble size in turn is a function of liquid seal height and design of the inlet pipe in the seal drum. A simple cylinder with one end dipped in the seal liquid may suffice for large flow rates of flare gases, which may be observed in case of any eventuality. At higher flow of the flare gases, the seal fluid in the inlet pipe would always be pushed below to provide exit area for the gases. However, for most of LSD operations, the flare gas flow rate is about 10% of the design. Therefore, the exit end of the inlet pipe is designed such that the available gas exit area increases with increase in flare gas flow rate. It can be observed from Figure 2 that the exit end of the inlet pipe has circular holes, followed by rectangular and triangular notches, respectively. At lower flow rates, the exit area provided by the circular holes may suffice, and the gas would escape from them, causing little disturbance to the seal fluid below it. If the gas flow rate increases, rectangular and triangular notches would open for the gas to exit. Thus, sufficient exit area must be provided for the flare gases passing through the LSD. Proper design of the exit end of the inlet pipe helps to avoid flare puffing and knocking. Pendulum-like motion of liquids is termed as sloshing. Sloshing happens in moving fluid (milk, water, petroleum products, etc.) containers. It happens because of frequent acceleration and deceleration of these vehicles. Sloshing can happen due to the

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bubble formation and bursting. Sloshing in seal drums happens through this phenomenon. Frequently, baffles, termed as antisloshing baffles (ASB), are used for preventing sloshing. ASBs are very common in moving containers, for example, fuel tankers and fuel chambers of satellites. Different designs of the ASBs are employed. Figure 2 shows an ASB, which is a cylinder with a large number of perforated holes placed around the exit end of the inlet pipe. The ASB is intended to limit the fluid turbulence within a small distance so that the bulk of the seal fluid is largely undisturbed. Turbulence generated due to high velocity can lead to dislodging of internals (ASB, weir plate, etc.) present in the liquid seal drums. The diameter of the ASB shown in Figure 2 is very critical for its proper functioning. Low diameter can lead to Taylor bubble formation in the annular region formed between the ASB and outer wall of the inlet pipe. This Taylor bubble may disturb the mechanical integrity of the ASB. Large diameter ASB would increase the turbulent region in the seal drum. The ASB must be installed with sufficient mechanical support; otherwise, it can produce unwanted vibrations and also damage the inlet pipe. In the present work, CFD (based on volume of fluid concept) as well as theoretical modeling have been used for deciphering the hydrodynamics in two different designs (designated as design-1 and design-2) of the liquid seal drums. Section 2 discusses the CFD methodology, along with results and observations obtained through CFD for design-1. Section 3 discusses the details of the 1D model used in this study. Results and observations for CFD simulation of design-2 have been discussed in section 4. The performance of these two designs with respect to liquid level fluctuation has been compared in section 5. Finally, conclusions and understanding obtained through this study have been summarized in section 6.

2. CFD ANALYSIS OF DESIGN-1 As the present study required capturing of the gasliquid interface, the volume of fluid (VOF) model (along with realizable kε model for turbulence) in FLUENT has been used for CFD simulations. The details of VOF model have been summarized in Appendix 1.9 The length scale ratio (maximum/minimum) in the present study was very large. The seal drum volume was about 180.5 m3. Hence, meshing the drum with a uniform grid size of even 10 mm would result in about 180 million hexahedral cells. The smallest length scale in the geometry is 1.2 mm. This is the orifice diameter on the gas inlet pipe. Hence, to capture the geometry of this orifice, grid size must be smaller than this. This would lead to very large number of grid points. Also, VOF calculations are inherently slow as they capture the interface in each and every computational cell. Thus, 3D simulation would require tremendous computing power and memory requirement. Hence, we resorted to 2D simulations with grid size varying from 0.4 mm (near the orifice) to 15 mm (in the region away from the inlet section). Even for 2D geometry and mesh grading, this configuration resulted in 0.3 million grids. This variation in grid size was found to represent the velocity gradient in the inlet section appropriately. Two-dimensional (2D) approximation of the seal drum design along with the internals was created in GAMBIT. In 2D, the ASB was approximated as a line with vertical perforations. The length of these perforations was equal to the orifice diameter. 2D-structured mesh with more grid density in the area around ASB has been created in the seal drum geometry as described above. 1074

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Figure 4. Contours of pressure (A), horizontal (B), and vertical velocity (C) in design-1.

Figure 3. Volume fraction contours of water at different time intervals for earlier design.

Unsteady-state VOF simulations were conducted with realizable kε model for turbulence. Water and flare gas were taken as the two fluids. Implicit body force formulation was activated to account the effect of body forces. PISO scheme was used for pressurevelocity coupling. This scheme is robust as compared to SIMPLE. Geo-reconstruct scheme was used for discretizing the volume fraction equation. This scheme gives a sharper gas liquid interface as compared to other techniques. PRESTO scheme was used for pressure discretization. This is the recommended scheme for VOF calculation in FLUENT. Explicit scheme was used for solution of the volume fraction equation. Momentum, turbulent kinetic energy, and turbulent kinetic energy dissipation rate were discretized using the second-order upwind scheme. Solution was initialized with the seal drum completely filled with flare gas. The water phase was later patched to the desired seal height.

Parallel simulation capability of FLUENT was used for obtaining the solution. The simulation was continued on 8-nodes of a parallel processing UNIX server. An under-relaxation factor (URF) of 0.2 was used for pressure. URF was taken as 0.4 for all other parameters. A time step of 1 104 was used for the simulations. At each time step, the residues were falling below 1 104, ensuring convergence. The solution was continued for four passes of flare gas through the seal drum. This is essential to attain a quasi-steady state. Each solution took about a week. The simulation was continued on 8-nodes of a parallel processing UNIX server. Each solution took about a week. Figure 3 shows the volume fraction contours of water at different time intervals for a flare gas flow rate of 4 ton/h. Red color shows that the volume fraction of water is 1.0, whereas blue color indicates the regions where volume fraction of water is 0 (i.e., volume fraction of flare gas is 1.0). Other regions show a mixture of water and flare gas. Figure 3A shows the initial situation in the seal drum. As the simulation progresses, the effect of gas flow in the seal drum is calculated and has been presented in Figure 3BE. It can be observed from Figure 3B that a large gas Taylor bubble is forming in the annular region formed between the wall of the inlet pipe and the ASB. As the Taylor bubble rises to the interface, it forces the seal fluid to pass through the holes in ASB. Also, a part of the liquid is lifted by the Taylor bubble. This liquid falls on the ASB when the gas Taylor bubble bursts at the gasliquid interface. Figure 4AC, respectively, shows the contours of pressure, horizontal, and vertical velocity in the seal drum for flare gas load of 4 ton/h and flow time of 1.46 s. 1075



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Figure 5. Pictorial representation of liquid motion due to movement of Taylor bubble.

It can be observed from this figure that the CFD model is able to predict the static head in the liquid. The blob-like structure in Figure 4A shows the location of liquid slug near the gasliquid interface. Figure 4B shows the contours of variation of horizontal velocity in the LSD. It can be observed from this figure that the large velocity gradients exist in the annular region formed between the wall of the inlet pipe and the gasliquid interface. Maximum horizontal velocity (about 46 m/s) exists when the gas comes out of the inlet pipe. This figure also shows that the ASB is being hit by a horizontal velocity of about 1.5 and 9 m/s at the bottom and top ends, respectively. Thus, a torque directing toward the weir plate would be exerted on the upper end of the ASB. The enlarged view of the velocity vectors around the exit end is shown to the right of Figure 4B. It shows the velocity vectors of gas as it passes through the apertures provided in these designs. It can be observed from this figure that, due to the presence of the antisloshing baffles, the flow in design-1 turns vertical as soon as it exits the gas inlet pipe. Figure 4C shows the contours of the vertical velocity in the LSD. It can be observed that the Taylor bubble rises very rapidly in the annular region. It can be observed that the vertical velocity becomes as high as 43 m/s for a gas load of only 4 ton/h. Vertical velocities would exert drag force on the ASB. As the flare gas load to the LSD changes, so does the forces associated with horizontal and vertical velocities acting on the ASB. The ASB must be mechanically strong enough to withstand these forces.

3. 1D MODEL FOR BUBBLE SIZE, LEVEL FLUCTUATIONS, AND STRESSES As discussed above, CFD analysis showed that the formation and break up of large sized bubbles (also called as Taylor bubbles)

Figure 6. Schematic of bubble bursting at the gas liquid interface toward the upper end of ASB.

is the main reason for liquid level fluctuations. For detailed calculation of the flow regime, bubble dimensions, and amplitude of liquid level fluctuation, the 1D model has been adopted. Govier and Aziz1 have presented an excellent treatise on flow of complex mixtures in pipes. The 1D model adopted has used the information compiled by them. Frequency (ω) and amplitude (Amp) of liquid level fluctuation is related to the Taylor bubble size (de) through the following equations: ln ω ¼ 1:865 3 d1:4 e

ð1Þ

Amp ¼ k 3 d2e

ð2Þ

Equations 1 and 2 suggest that an increase in bubble diameter decreases the frequency of level fluctuation but results in an 1076



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Figure 7. Schematic of design-2 of liquid seal drums.

Figure 9. Contours of pressure (A), horizontal (B), and vertical velocity (C) in design-2.

perforated cylinders. The top section of both of these cylinders is open, whereas the bottom is welded to the seal drum. Cylindrical surface has a number of holes (diameter 20 mm) on it. Major steps of calculation and equations have been summarized in Appendix 2. Calculation of shear stress showed that maximum shear stress exerted on ASB of design-1 exceeds the allowable limit of welding joints. This showed the probability for dislodging of ASB in design-1.

Figure 8. Volume fraction contours of water at different time intervals for design-2.

increase in the amplitude of these fluctuations. Internals present in the seal drum are subjected to different forces due to movement of the water level and bursting of bubbles. The 1D model has also been used to calculate the force exerted on the ASB due to water displacement (Figure 5) and Taylor bubble bursting (Figure 6). Rectangular square areas consisting of small circles in Figure 5 show that the ASB as well as concentric inner pipe are

4. CFD SIMULATION RESULTS FOR DESIGN-2 CFD simulation for design-2 of the seal drum (Figure 7) was carried out by using the same methodology as used for design-1. Design-2 differs from design-1 in two aspects; it does not hasve ASB, and it has horns in addition to the central pipe for releasing the gas in the water pool. 0.3 million grid points were generated for design-2. Figure 8 shows the volume fraction contours at different time intervals for design-2 of LSD for flare gas flow rate of 4 ton/h. Red color shows that the volume fraction of water is 1.0, whereas blue color indicates the regions where volume fraction of water is 0 (i.e., volume fraction of flare gas is 1.0). Other regions show a mixture of water and flare gas. Figure 8A shows the initial situation in the seal drum. As the simulation progresses, the effect of gas flow in the seal drum is calculated and has been presented in Figure 8BE. It can be observed from Figures 3 and 8 that in design-2 smaller bubbles are formed as compared to design-1. These smaller bubbles are easily escaping to the gasliquid interface without much 1077



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Table 1. Comparison of Pressure and Velocities in Design-1 and Design-2 parameter maximum pressure in the seal drum (bar) maximum horizontal velocity (m/s) maximum vertical velocity (m/s)

design-1 1.5 46 74

design-2 1.2 32 29

disturbance to the seal fluid. Figure 9AC, respectively, shows the contours of pressure, horizontal, and vertical velocity in the seal drum for a flare gas load of 4 ton/h and a flow time of 1.46 s. Figure 9A shows the variation in the pressure across the seal drum diameter. It can be observed from this figure that the CFD model is able to predict the static head in the liquid. Figure 9B shows the contours of variation of horizontal velocity in the LSD. It can be observed from this figure that the flare gas is preferentially exiting from one of the horns. The liquid in this seal drum is oscillating (it can be observed from Figure 8), and the other horn would be used once the liquid level falls on its side. The oscillation may be because of the absence of ASB in this design. Maximum horizontal velocity (about 32 m/s) exists when the gas comes out of the inlet pipe. The enlarged view of the velocity vectors around the exit end is shown to the right of Figure 9B. It shows that for design-2, gas jet exiting the inlet pipe penetrates longer in the liquid pool before turning ups. Figure 9C shows the contours of the vertical velocity in the LSD. The maximum vertical velocity is about 29 m/s. A comparison of vertical velocities in Figures 4C (for design-1) and 9C (for Design-2) clearly demonstrates the effect of ASB. Figure 4C shows that the vertical velocity is about 43 m/s in the zone between the gas inlet pipe and ASB. However, vertical velocity for flow with design-2 is about 20 m/s. Table 1 summarizes the maximum pressure and velocity for the two designs for the flare gas flow rate of 4 ton/h at 1.46 s.

5. COMPARISON OF DESIGN-1 AND DESIGN-2 It can be observed from Figures 3, 4 (for design-1) and Figures 8, 9 (for design-2) that the hydrodynamics in the two designs of seal drums differ. These figures depict the volume fraction, pressure, horizontal, and vertical velocities for the two seal drum designs. Volume fraction contours show that large slugs of flare gases are formed in design-1, whereas no such slugs are observed in design-2. The ASB provided in design-1 is causing hindrance to the escape of the large bubbles. A number of bubbles combine to form a large Taylor bubble. Movement of Taylor bubble through the annular region leads to high horizontal as well as vertical velocities in design-1 as compared to design-2. ASB is designed to reduce the turbulence, which is created due to displacement of seal fluid. In design-1, a large quantity of fluid is lifted up and falls on the upper end of the ASB when the Taylor bubble bursts at the gasliquid interface. Only a small part of the seal fluid goes through the lower holes in ASB. Thus, the ASB is not being effectively used in deign-1. Besides, it helps in the formation of the Taylor bubbles. It can be concluded that design-1 is performing poorly due to the ASB. On the basis of the 1D model, it was estimated that reducing the liquid seal height and/or increasing the annular area will help in reducing the Taylor bubble formation. 1D analysis described above was used to predict the effect of variation of seal height on bubble diameter and level fluctuations. Figure 10 shows the effect of seal height on bubble diameter and level fluctuations for

Figure 10. Effect of seal height on bubble diameter and amplitude.

Figure 11. Effect of annular diameter on bubble diameter and amplitude.

design-1. It can be observed that an increase in liquid seal height leads to an increase in the bubble diameter as well as amplitude of level fluctuation. This implies that one should reduce the seal height to reduce the bubble size and amplitude of level fluctuation. However, reducing the liquid seal height is usually avoided as it increases the risk of backfiring in the flare system. An annular area is formed due to concentric orientation of gas inlet pipe and ASB. As the diameter of the ASB would increase, the diameter of the annular area would also increase. Thus, annular diameter refers to the gap between the gas inlet pipe and ASB. The effect of increasing the annular diameter (distance between the seal drum inlet pipe and ASB) has been shown in Figure 11 for design-1. It can be observed that increasing the annular diameter leads to reduction in bubble diameter as well as amplitude of liquid level fluctuations. Point A in Figure 11 shows the location for the geometry used for CFD simulations. It can be observed that bubbles of size 33 cm are forming in design-1. It can be observed from Figure 11 that bubble diameter as well as amplitude of level fluctuations reduce by increasing the annular diameter. However, increasing the annular diameter beyond 3 m does not reduce the bubble size beyond 20 cm. This bubble size is very large as compared to the size of the bubble (3.4 cm) obtained with design-2 (calculated from the 1D model). Small diameter bubbles in design-2 may also be formed due to the extra exit area provided by the horn type structure. It can be concluded from the above analysis that design-2 is superior to design-1 as lower diameter bubbles (resulting in lower liquid level fluctuations) are formed. Figure 12 shows the reduction in liquid level fluctuations in design-2 as compared to design-1. The level fluctuations 1078



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since then. Internals of deisgn-1 used to get damaged every 23 months, leading to operating problems. Overall, design-2 of the liquid seal drum showed considerable improvement in performance as compared to design-1, leading to reliability improvements and substantial monetary benefits.

Figure 12. Liquid level fluctuations in seal drums before and after modification.

were monitored on the plant DCS panel for the period having an average flow of flare gas around 4 ton/h. The peak value of level fluctuations reduced from 9% to 3%. The standard deviation also reduced from 8.47 to 3.74. Bubble size was not measured in the seal drum. However, for liquid level fluctuations, the 1D model predicted that the fluctuations would reduce from 9% to 4%, whereas field data showed that level fluctuations reduced from 9% to 3%. Because level fluctuations are due to movement of bubbles, a good match for this parameter infers that bubble sizes would be comparable.

6. CONCLUSIONS In the present work, a CFD model has been developed for deciphering the hydrodynamics in a liquid seal drum of a refinery flare system. A theoretical model based on Taylor bubble phenomenon has been adopted for quantification of bubble size and level fluctuations associated with them. It was observed that at low flare loads, puffing is linked to bubble diameter and liquid seal height for both designs of liquid seal drums. A significant amount of slug flow happens in design-1, which could be visualized through a multiphase CFD model. The slug flow leads to explosion of large size Taylor bubbles on water surface. The force thus generated can be calculated through the 1D model developed in this study. Chances for formation of Taylor bubble are minimized in design-2 as it does not have ASB. Also, horns in design-2 provide additional release area for the flare gas, which helps in uniform passage for the gas. Thus, design-2 has a substantially minimized risk of internal damage. The level fluctuations depend on the size of bubble that is formed when the flare gas passes through the liquid seal. This will depend on the liquid seal height, gas inflow, and the design of internals. Therefore, the effort was to minimize the bubble size formed. Reduction in level fluctuation from 9% to 3% is more than satisfactory, and trying to go below this may not help the plant in a great way. Design-2 of the seal drum internal has been in use for more than a year, and problems such as damage to internals as well as puffing and knocking have not been observed

’ APPENDIX 1: DETAILS OF CFD MODEL CFD simulations in this study have been carried out using the volume of fluid (VOF) model of FLUENT 6.3. The VOF model is a surface-tracking technique applied to a fixed Eulerian mesh. The VOF formulation relies on the fact that two or more fluids (or phases) are not interpenetrating. For each additional phase added to the model, an additional variable for the volume fraction (α) of the phase in the computational cell is introduced. In each control volume, the volume fractions of all phases sum to unity. The fields for all variables and properties are shared by the phases and represent volume-averaged values, as long as the volume fraction of each of the phases is known at each location. Thus, the variables and properties in any given cell are either purely representative of one of the phases, or representative of a mixture of the phases, depending upon the volume fraction values.9 The tracking of the interface(s) between the phases is accomplished by the solution of a continuity equation for the volume fraction of one (or more) of the phases. For the qth phase, this equation has the following form: " # n 1 ∂ ðαq Fq Þ þ ∇ 3 ðαq Fq B v q Þ ¼ Sαq þ ðm_ pq m_ qp Þ Fq ∂t p¼1

∑

ðA1:1Þ where mqp is the mass transfer from phase q to phase p, and mpq is the mass transfer from phase p to phase q. By default, the source term on the right-hand side of eq 1, Sαq, is zero, but it can be specified as a constant or user-defined mass source for each phase. In the present study, the source term value has been taken to be zero. The volume fraction equation is not solved for the primary phase; the primary-phase volume fraction is computed on the basis of the following constraint: n

∑ αq ¼ 1 q¼1

ðA1:2Þ

The properties appearing in the transport equations are determined by the presence of the component phases in each control volume. For a two-phase system, as in the present case, if the phases are represented by the subscripts 1 and 2, and if the volume fraction of the second of these is being tracked, the density in each cell is given by F ¼ α2 F2 þ ð1 α2 ÞF1

ðA1:3Þ

All other properties (e.g., viscosity) are computed in this manner. A single momentum equation is solved throughout the domain, and the resulting velocity (v B) field is shared among the phases. The momentum equation, shown below, is dependent on the volume fractions of all phases through the properties F and μ. ∂ v B vÞ ðF v Þ þ ∇ 3 ðF B ∂t B

¼ ∇p þ ∇ 3 ½μð∇ B v þ ∇B v T Þ þ F gB þ FB

ðA1:4Þ

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In the case of turbulence quantities, a single set of transport equations is solved, and the turbulence variables (e.g., k and ε or the Reynolds stresses) are shared by the phases throughout the field. The transport equations for turbulent kinetic energy (k) and turbulent kinetic energy dissipation rate (ε) in the realizable kε model used in the present study are as follows: " # ∂ ∂ ∂ μt ∂k ðFkÞ þ ðFkuj Þ ¼ μ þ ∂t ∂xi ∂xi σk ∂xj þ Gk þ Gb Fε YM þ Sk

∂ ∂ ∂ ðFεÞ þ ðFεuj Þ ¼ ∂t ∂xj ∂xj

μ þ

μt ∂ε σ ε ∂xj

where

η k and η ¼ S η þ 5 ε

In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy, and YM represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. This term is negligible in the present case as the seal drum operates at close to atmospheric pressure. C2 and C1ε are constants with values as given in the FLUENT manual. σk and σε are the turbulent Prandtl numbers for k and ε, respectively. S k and Sε are user-defined source terms, which have been taken to be zero in the present case as movement of gas through the liquid pool is the only factor resulting in turbulent flow. No additional source of turbulence is present. Solution of eqs A1.1A1.6 would give the values of velocity, volume fraction, and turbulent energy and its dissipation rate in each of the control volume in the computational domain. Velocities obtained through the CFD simulations were used in the 1D model for calculating the forces exerted on the ASB.

’ APPENDIX 2: CALCULATION SEQUENCE FOR THE 1D MODEL 1. Calculation of Bubble Volume Formed at Zero Frequency. The volume of bubble formed at orifice with zero bub-

ble frequency can be calculated from equation A1:c ϑb0 ¼ 0:0942 3 sinhð1:64 3 Do Þ

ðA2.1Þ

2. Calculation of Frequency of Small Bubbles Formed at Orifices. If the frequency of bubble generation at the orifice is ω,

then the bubble volume (ϑb0) can be obtained from eq A2.2: ϑb0 ¼ ϑbo 3 ð1 þ 0:075ωÞ

3. Regime Calculations. Flow regime in the seal drum is calculated using two methods: (1) by calculating bubble volume fraction (eq A2.4) in the annular zone (if EG ≈ 1, signifies slug flow) and (2) by calculating slug flow transition velocity (eq A2.7).

g ΔF 3 d2e Eo ¼ 3 σ

E̅ G ¼ ðA1:6Þ

C1 ¼ max 0:43,

ðA2:3Þ

ðA2:4Þ

It has been reported by Crowe (2006) that bubbles assume the shape of a spherical cap at high Eo (typical >40). The Eotvos number was calculated using eq A2.4 to verify this observation. The bubble volume fraction is calculated from eq A2.5:

#

ε2 ε pffiffiffiffiffi þ C1ε C3ε Gb þ Sε þ FC1 Sε FC2 k k þ υε

Q ¼ n 3 ϑb0 3 ω

ðA1.5Þ

and "

Total volumetric flow rate (Q) of the flare gas is related to ω through the following relation A2.3:

43Q π 3 D2 3 V bs

The bubble rise velocity is calculated from eq A2.6: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g 3 ΔF 3 de V bs ¼ 0:715 3 FL

ðA2:5Þ

ðA2:6Þ

4. Regime Verification. Hydrodynamic regime is further verified by comparing bubble to slug transition velocity (VISG calculated from eq A2.7) for the gas phase with the superficial gas velocity (VSG): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g 3 ΔF 3 D I ¼ 0:56 3 VSL þ 0:16 3 VSG ðA2:7Þ FL

VSG < V ISG bubbling regime

ðA2:8Þ

VSG g V ISG slug flow regime

ðA2:9Þ

5. Taylor Bubble Rise Velocity, Film Thickness, and Volume Fraction. Many bubbles coalesce to form a big Taylor bubble

in slug flow. The Taylor bubble will almost cover the entire annulus diameter. The Taylor bubble rise velocity is calculated from eq A2.10. Vb ¼

VM þ Vf 3 2 3 ξ 123ξ

ðA2:10Þ

Further, the value is confirmed by eq A2.11. Vb ¼ 1:2 3 VM þ Vbs

ðA2:11Þ

The film thickness (δ) is a function of Vbs/VM, which can be calculated from Figure 8.42 on p 393 (Govier and Aziz, 1972). The Taylor bubble volume fraction is calculated as ratio of gasphase superficial velocity to bubble rise velocity (VSG/Vb). 6. Taylor Bubble Dimensions. Taylor bubble diameter is = D 2δ. Taylor bubble length and slug length are calculated from the following gas flow rate A2.12, Taylor bubble frequency A2.13, and bubble length A2.14:

ðA2.2Þ

Q ¼ ϑb 3 ω 1080

ðA2:12Þ dx.doi.org/10.1021/ie202683h |Ind. Eng. Chem. Res. 2012, 51, 1073–1082

Industrial & Engineering Chemistry Research ω¼

Vb Lb þ Ls

ðA2:13Þ

ðA2.14Þ

7. Force Calculation. Forces acting on the seal drum internals can be put into two categories: (a) force due to water displacement, and (b) force due to bursting of Taylor bubbles at the gas liquid interface. When the Taylor bubble moves through the annular region, it occupies a large chunk of the annular area. Therefore, the seal fluid is pushed out horizontally through the perforations in ASB. As the Taylor bubble rises through the annular region, it lifts a large quantity of seal fluid. Part of the seal fluid overflows the ASB, resulting in a torque at the upper end of the ASB. Calculated horizontal force due to water displacement = 110.5 kN. When the Taylor bubble bursts at the gas liquid interface, the remaining part of the lifted fluid falls on the upper end of ASB. Equations A2.9A2.13 can be used for calculating gas jet velocity, liquid droplet velocity, pressure wave magnitude, and ultimately force due to Taylor bubble burst on the ASB.

πm ¼

4 3 π 3 R 2b 3 Ffg 3 U 4 π 3 R 2b 3 ðΔPÞ2 ¼ Km Ffg 3 C C

"

ðΔPÞ2 U ¼ 4 3 F2fg 3 K m

V drop ¼ U 3

’ AUTHOR INFORMATION Corresponding Author

VSG 3 Ls þ n 3 D 3 ðVbs þ CO 3 VM Þ m 3 ðVbs þ CO 3 VM Þ VSG

Lb ¼

ARTICLE

ðA2:15Þ

#1=4 ðA2:16Þ

sffiffiffiffiffiffi Ffg

ðA2:17Þ

FL

ΔP ¼ F 3 C 3 ΔV

ðA2:18Þ

8. Stress Calculation. The following equations are used to calculate stress values on ASB due to water displacement and Taylor bubble burst.

shear stress τ ¼

’ NOMENCLATURE A = area for gas flow (m2) Amp = amplitude of fluctuation (m) C = sound velocity (m/s) co = constant () di = inside diameter of annular space between gas inlet pipe and ASB (m) do = outlet diameter of annular space between gas inlet pipe and ASB (m) de = bubble diameter (m) Do = orifice diameter (m) D = diameter of annular region (m) Eo = Eotvos number () EG = bubble volume fraction () e = eccentricity (m) F = force (N) g = acceleration due to gravity (m/s2) k = constant () Km = constant () Lb = Taylor bubble length (m) Ls = slug length (m) M = bending moment (N/m2) m = constant () n = no. of phases/orifices () ΔP = effective seal pressure drop (N/m2) Q = volumetric flow rate of flare gas (m3/s) Rb = bubble radius (m) U = free stream velocity/gas velocity (m/s) Vb = Taylor bubble rise velocity (m/s) Vdrop = liquid droplet velocity in gas jet (m/s) VM = average slug velocity (m/s) Vf = liquid film velocity (m/s) Vbs = bubble rise velocity (m/s) VSL = superficial liquid velocity (m/s) VSG = superficial gas velocity (m/s) VISG = gas-phase transition velocity (m/s) ΔV = change in velocity (m/s) Z = section modulus (m) Greek Symbols

F A

bending stress σb ¼

*Tel.: (0288)-2312314. Fax: (0288)-2312350. E-mail: asit.das@. ril.com.

ðA2:19Þ M Z

ðA2:20Þ

bending moment M ¼ F 3 e

ðA2:21Þ

section modulus for pipe Z ¼ 0:0982 3 maximum shear stress τmax ¼ 0:5 3

do4 di4 do

ðA2:22Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σ2b þ 4 3 τ2 ðA2:23Þ

σ = surface tension (N/m) δ = film thickness (m) σb = bending stress (N/m2) FL = density of seal fluid (kg/m3) Ffg = density of flare gas (kg/m3) ΔF = density difference between seal fluid and flare gas (kg/m3) ω = frequency of bubble generation (s1) ϑ*b0 = volume of the Taylor bubble formed at zero bubble frequency (m3) ϑb0 = bubble volume (m3) τ = shear stress (N/m2) τmax = maximum shear stress (N/m2) ξ = a function of film thickness () πm = acoustic power of single bubble (W) 1081



ARTICLE

’ REFERENCES (1) Govier, G. W.; Aziz, K. The Flow of Complex Mixtures in Pipes; Van Nostrand Reinhold Co.: Canada, 1972. (2) Richards, J. F.; Terrell, W. L. Baffle construction for the flare seal drums. U.S. patent no. 3691732, 1972. (3) Michelson, H. D.; Levy, R. M. Liquid seal system for minimizing flow pulsing in flare seal drums. U.S. patent no. 4844844, 1989. (4) Seebold, J. G. Flare liquid seal drum surging: Prediction, prevention and Proof. AFRC-JFRC, Joint international combustion symposium Maui, Environmental control of combustion processes: Innovative technology for the 21st Century, Walea Marriott Resort, October 1013, Maui, HI, 2004. (5) Ibrahim, R. A. Liquid Sloshing Dynamics: Theory and Applications; Cambridge University Press: MI, 2005. (6) American Petroleum Institute, 5th ed.; API Standard 521, Pressurerelieving and Depressuring Systems, 2008. (7) Shell Design and Engineering Pratices, Shell DEP No. 80.45. 10.10, Pressure relief, emergency depressuring, flare and vent systems, 1996. (8) Parry, C. F. Relief Systems Handbook; Institute of Chemical Engineers, UK, 1992; Chapter 4. Total relief systems; pp 7071. (9) Fluent. FLUENT 6.3 Documentation; Ansys Inc.: Pune, India, 2006.

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Multiphase CFD Simulation of Flow Inside Liquid Seal Drums of the

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