Dry Pressure Drop Prediction within Montz-pak B1-250.45 Packing

Research Note pubs.acs.org/IECR

Dry Pressure Drop Prediction within Montz-pak B1-250.45 Packing with Varied Inclination Angles and Geometries L.M. Armstrong,† S. Gu,*,†,‡ and K.H. Luo†,¶ †

Energy Technology Research Group, School of Engineering Sciences, University of Southampton, Southampton, SO17 1BJ, United Kingdom ‡ School of Engineering, Cranfield University, Cranfield, Bedfordshire, MK43 0AL, England ¶ Centre for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Thermal Engineering, Tsinghua University, Beijing 100084, China ABSTRACT: Structured packings are used to increase the surface area and promote gas−liquid contact in many chemical processes, including carbon capture. Computational fluid dynamics and performance prediction methods have the ability to aid the optimization of the structured packing designs to aid the heat and mass transfer while minimizing the pressure drop. The present work introduces pressure drop correlations that determine frictional pressure loss between Montz-Pak B1-250.45 structured packing sheets based on the inclination angle and channel geometry of the sheets. CFD simulations are carried out on the packing and are validated against published experimental data.

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INTRODUCTION Structured packing is widely used in industry for chemical processes which require high gas/liquid contact, including separation and carbon capture. This is due to high surface areas of the processes; however, they incur large pressure drops. Optimising the packing designs can ensure a low pressure drop yet promote heat and mass exchange, but this can only be done once the flow dynamics are clearly understood, which is achievable using computational fluid dynamics (CFD) modeling. Accurate CFD modeling of the whole reactor is not currently possible due to the multiple scales found within the reactor. The liquid flow along the packing walls requires microscopic analysis to determine characteristics such as the liquid hold up and gas/liquid interface velocities. Mesoscale modeling considers the flow dynamics between the packing sheets, while the flow influences due to reactor walls, inlets, distributors, etc., are considered at the macro-scale level. Accurately resolving all three scales using a single mesh, even for a lab-scale reactor, would be impossible.1 Volume of fluid (VOF) methods have been used to determine the gas−liquid interactions at the microscale using multiphase flow1−6 and large sections of structured packing have been simulated to determine the effects of turbulence within the bed.7,8 Periodic modeling has been used for a variety of different packing arrangements by a number of researchers.6,9−11 This method allows CFD simulations to be performed on small representative elementary units (REU) which can focus on specific regions that contribute to the overall pressure loss. These REUs compared well with the pressure drop for a large section of packing.12 Petre et al.10 analyzed the four leading contributors to pressure loss including the flow entrance, colliding jet streams, direction change at “elbows” and also wall presence. Correlations have been developed to predict the frictional pressure loss across these regions.9,10,12−14 The region © 2013 American Chemical Society

responsible for the highest frictional pressure drop is the colliding jet streams from opposing flows in the open crisscrossing junctions. The effects of the channel base and the channel height have been considered and validated the results with simulations for different geometries.12 The effects of inclination angle have been considered for standard packing geometries without modification to the geometries.10 A correlation has also been developed for the pressure loss due to direction changes, that is, the loss at “elbow” junctions and wall presence.14 The inclination angle is commonly acknowledged to exhibit a strong impact on the flow dynamics within structured packing. Angle variation was considered experimentally15 yet CFD simulations are consistently performed on elements where the packing is set to the standard inclination angle of 45° or 60° so consideration needs to be made for the varied angles. The present work performs mesoscale periodic simulations of 3D structure packing elements with modified inclination angles. The pressure drop data obtained are validated with experimental data.14 Two frictional loss correlations are developed and validated with a range of simulated data for different inclination angles and channel geometries. The first correlation signifies the impact that the inclination angle has on the frictional pressure drop, which is usually neglected. The second incorporates these findings, along with geometrical results from the literature, which successfully predicts the pressure drop of a packing design that lies outside the original data set used to predict the correlation. Received: Revised: Accepted: Published: 4372

April 30, 2012 February 21, 2013 March 4, 2013 March 4, 2013 dx.doi.org/10.1021/ie301120u | Ind. Eng. Chem. Res. 2013, 52, 4372−4378

Industrial & Engineering Chemistry Research

Research Note

Figure 3. Comparison of simulated frictional and correlated drag pressure drops with experimental data from Montz-pak B1-250.45.14

Table 2. Coefficients of Best Fit for the Predictive Pressure Drop Constants in eq 7, eq 10, and eq 11

Figure 1. (a) Representative section of packing, (b) REU with periodic boundaries, and (c) structured elements with different corrugated inclination angles.

i

Γi

θi

ni

1 2 3 4

0.242 0.414

15.195 0.525 0.072 −4.318

0.002 0.762 4.248

Conservation of momentum: ∂(ρυi) ∂ + (ρυiυj) ∂t ∂xj ⎡ ∂υj 2δi , j ∂υi ⎞⎤ ∂p ∂ ⎢ ⎛⎜ ∂υi ⎟⎥ − + μ⎜ + ∂xi ∂xi ∂xj ⎢⎣ ⎝ ∂xj 3 ∂xi ⎟⎠⎥⎦ ∂ + ( −ρυiυj) + ρgi ∂xj

=−

where ρ, υ, and p represent the density, velocity, and pressure, respectively. The use of CFD to simulate the gas and liquid flow within an absorber consisting of structured packing is a difficult challenge due to the different scales that are present: (i) Macroscale which considers the influences from reactor walls, inlets, distributors etc., on the gas flow. (ii) Mesoscale which analyses the flow dynamics between Representative Elementary Units (REU) of the packing. (iii) Microscale which determines nearwall characteristics, for example, liquid hold up and liquid velocity. The dominating region responsible for pressure drop is the mesoscale region as the gas traverses between the layers of structured packing losing pressure due to four important regions: entrance regions, criss-crossing junctions, transition between layers, and channel-wall transition.10 Therefore the present work will focus on the mesoscale effects of the gas flow between the packing sheets. A dry model is considered in the present case as the contribution to pressure drop from the liquid presence is minimal. Furthermore, the liquid presence would require extensive grid refinement in the near-wall regions which can be highly computationally exhaustive. However, we are currently simulating multiphase cases for comparative purposes with the present dry case and previous flow assumptions made using moving wall boundary conditions.1

Figure 2. Pressure drop over a range of f-factors performed with different mesh sizes.

Table 1. Periodic Element Properties inclination angle

element height (m)

element width (m)

number of cells

60° 50° 45° 40° 30°

0.0450 0.0350 0.0318 0.0294 0.0260

0.0260 0.0294 0.0318 0.0350 0.0450

437079 410349 401032 410501 438788

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CFD MODELING CFD uses numerical methods to solve fluid flow problems and has been applied successfully to many industrial problems. The present work is an isothermal nonreactive dry case, that is, gas only, so the exchange of thermal energy is not considered. The conservation equations for a single phase model16 are given as Conservation of mass: ∂ρ ∂ + (ρυi) = 0 ∂t ∂xi

(2)

(1) 4373

dx.doi.org/10.1021/ie301120u | Ind. Eng. Chem. Res. 2013, 52, 4372−4378


Research Note

Figure 4. Comparison of simulated data at various inclination angle and velocities with the correlations of (a) Said et al.;12 (b) the present work, using eq 7, eq 10, and eq 11.

position with respect to the wall. A full description of the k−ω model is available from the literature,18 as the model itself is very extensive. Periodic Element Construction. The commercial Montzpak B1-250.45 packing uses unperforated corrugated metal sheets which are positioned with an inclination angle of 45° from the horizontal. Representative elementary units (REU) are the smallest elementary structures capable of capturing the flow dynamics within each of the important flow regions responsible for pressure drop. A periodic model of an REU is more efficient in comparison to simulations of large arrays of packing as less cells are required as it can simulate the crisscrossing phenomena across coupled faces such that it behaves similarly to part of a larger array of structured packing, as shown in Figure 1a. Figure 1b demonstrates the periodic concept as flow leaving the top of the element through a channel of the front sheet; that is, the green arrows, would be reintroduced to the front channel at the base of the REU. Geometric properties of Montz-pak packing include a base width of 0.0225 m, height of 0.012 m, surface area of 244 m−1, and porosity of 98%. The corrugated inclination angle, usually

Table 3. Coefficients of Best Fit for the Predictive Pressure Drop Constants in eq 7, 12, and 13 i

Γi

θi

ni

1 2 3 4 5 6 7 8

0.573 0.462 0.240 1.712

0.004 11.139 −9.868 −13.120 24.735 −5.232 8.751 −3.766

0.219 0.939 1.059

The turbulent flow behaviors, particularly at the crisscrossing junctions, are considered using the shear-stress transport (SST) k−ω model. Comparisons have been made for a range of turbulence models,12,17 and it was found that the SST k−ω model was better suited for simulating flow between the structured packing. This is due to its ability to combine the near-wall model of the standard k−ω model with the capabilities of the k−ε model for the regions further in the channels. A blending function is used to establish the flow 4374



Research Note

45°, is modified to consider the angles 60°, 50°, 40°, and 30° from the horizontal plane, as displayed in Figure 1c. Figure 2 displays the frictional pressure drop obtained using three mesh cell sizes, 1.0, 0.75, and 0.5 mm in a 45° element consisting of 142210, 401032, and 1121078 tetrahedral cells, respectively. The computational times ranged from several hours for the 1.0 mm mesh to a couple of days for the 0.5 mm mesh. The different mesh sizes produced similar results with increasing f-factors, which is a gas flow factor defined as Ug√ρg, where Ug is the superficial gas velocity. The maximum error at an F-factor of 6 (kg/m3)0.5 m/s between the 0.75 mm and 0.5 mm grid and the 1.0 mm and 0.5 mm grid are 3.36% and 5.46%, respectively. The remaining simulations are performed using the 75 mm mesh to maintain the accuracy over the coarser grid yet produce faster results than the more refined grid. The optimum element to mesh is the 45° element due to the uniform positioning of the cells. Increasing or decreasing the inclination angle from 45° increases the number of cells as further refinement needs to account for more acute and obtuse bisections of the opposing channel walls. As expected, the 30° and the 60° elements and the 40° and 50° elements have similar cell numbers as the elements have the same dimensions but with different orientations. Figure 2 gives information of the REU geometries and cell numbers. Simulation Boundary Conditions. The structured packing walls had no-slip boundary conditions and the upper/lower and left/right faces were periodically linked to allow for flow in the y-direction and x-directional, respectively. As performed previously by Said et al.12 a gap of 0.05 mm was placed between the sheets to aid the meshing process in regions where opposing channel walls are in contact. The air density was 1.225 kg/m3 and viscosity was 1.7894 × 10−5 kg/s m. Development of Pressure Drop Correlations. Total Pressure Drop. Olujić14 categorized the different pressure drop factors into two components, the frictional component, ξf, and the drag component, ξdc. The dominating frictional component occurs due to the collisional jets in the open criss-cross junctions, and the drag component is a result of directional change, that is, at “elbows” and walls. They also included a third component which was the pressure drop due to gas/liquid interaction but this is negligible in the present work as a dry model is used. They produced a correlation to determine the pressure drop for the drag component, which has been applied by researchers:10,12,14

ΔP = (ξf + ξdc)

⎛ 1 ⎞ ρg uGe 2 ⎛ ΔP ⎞ ⎟⎟ ⎜ ⎟ = ξf ⎜⎜ ⎝ dy ⎠f ⎝ Ag sin α ⎠ 2

(5)

(6)

where the cross-sectional area is determined based on the channel base and height. The frictional loss coefficient, ξf, is taken to be12 ξf =

⎛ C1 C 2 ⎞n 3 ⎜ ⎟ + ⎝ Re n1 Re n2 ⎠

(7)

The Reynolds number is based on the channel height and the effective gas velocity, which relates the superficial gas velocity to the porosity of the structured packing and the inclination angle: ReGe =

uGe =

ρg uGehc μG

(8)

uG εg sin αg

(9)

The coefficients in eq 7, C1 and C2, are algebraic equations which incorporate the important factors that affect the pressure drop. Said et al.12 consider the effects of the channel base and height alone without inclination angle. To demonstrate the impact of inclination angle alone on the pressure drop these algebraic equations include only factors of inclination angle:

(3)

C1 = Γ1 cos(α)Γ2

(10)

C2 = θ1 cos(α)θ2 + θ3 cos(α)θ4

(11)

The coefficients ni, Γi, and θi, in eq 7, eq 10, and eq 11, respectively, were determined using a genetic algorithm19 which used simulated data for the different inclination angles, over a range of velocities, to determine the minimum deviation between the simulated and predicted pressure drops. The correlation coefficients are given in Table 2. Figure 4 compares the present correlation with that of Said et al.12 for simulated data of varied corrugation angles (corr: 30°− 60°) with different f-factors. It is clear that the inclination angle should be considered a larger factor than just its influence on the effective gas velocity, uGe, in eq 9. For this case the maximum error between the data and the correlation was 7.8%.

where uLs = 0 is the liquid superficial velocity which is negligible in the present work. ψ is the fraction of gas flow channels ending at the wall and is given by 0.5 ⎛ ⎛ hpe ⎞ hpe 2 ⎞ 2 ⎜dc − ⎟ + 2⎜ Ψ= ⎟ ⎜ 2 ⎟ 2 π ⎝ dc tan α ⎠ πdc tan α ⎝ tan α ⎠

2

The present simulated REUs do not include “elbows” or walls so the pressure drops obtained are frictional pressure drops due to the collisional criss-crossing jets. The pressure drop results of the simulated Montz-pak B1-250.45 structured packing element with an inclination angle of 45° can be added to the correlation pressure losses due to direction change and compared to the experimental data given by Olujić.14 Figure 3 shows that the sum of the frictional results from the present simulation with the direction pressure losses compare well with the experimental data. Frictional Pressure Drop. Since the loss of pressure due to friction accounts for the largest pressure drop within structured packing it is important to establish a correlation that correctly accounts for the different factors that affect the loss due to friction. The distributed frictional term for the pressure drop is given as a function of channel cross-sectional area and inclination angle:

⎛ 4092u 0.31 + 4715(cos α)0.445 Ls ξdc = 1.76(cos α)1.63 + Ψ⎜ ReGe ⎝ ⎞ + 34.19uLs 0.44(cos α)0.779 ⎟ ⎠

ρg uGe 2

2hpe

(4)

The total pressure drop across the packing column is given as the sum of the frictional and drag components multiplied by the effective gas velocity, uGe, and the gas density, ρg: 4375



Research Note

Figure 5. Parity plot of correlated predicted pressure drops (with factors for channel geometry included) vs the published simulated data of Said et al.12 performed at different channel heights.

Figure 6. Comparison of the correlation with present and published simulated data12 (a) for varied inclination angles, and various opening angles with channel heights (b) 6 mm; (c) 9 mm; and (d) 12 mm.

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However, this was carried out for the standard geometry and neglected the effects of varied opening angle and channel height. The genetic algorithm was rerun using an extensive range of geometry information from Said et al.12 and our inclination angle data with additional factors accounting for channel height and width in the constants, C1 and C2. The new coefficients for the best fit correlation are given in Table 3 and the new algebraic equations for C1 and C2, which are implemented into the loss equation, eq 7, are given by C1 = Γ1hcΓ2bcΓ3 cos(α)Γ4

(12)

C2 = θ1hcθ2bcθ3 cos(α)θ4 + θ5hcθ6bcθ7 cos(α)θ8

(13)

RESULTS

The parity plot in Figure 5 compares the simulated data with the predicted pressure drops using the new correlation for the different packing heights. A very good comparison can be seen with the majority of the prediction lying within 10% of the simulated data with a maximum error observed being 12.5%. The predicted pressure drops are compared with the published simulated data from Said et al.12 of different channel heights and opening angles and also with the present inclination angle data in Figure 6. The predictions agree very well for the different variables, particularly at lower f-factors where the flow is considered as laminar. Slight errors occur in regions of higher pressure drops, usually when the f-factor is high which concurs with the points lying outside the 10% regions in Figure 5. 4376



Research Note

Figure 7. Comparison of predicted correlation against simulated data for a packing with an opening angle of 120°, channel height of 12 mm, and an inclination angle of 60°.

the pressure drop for packing designs with different inclination angles, channel heights, and opening angles with a maximum mean relative error of 12.5%. The correlation was validated against a simulated structured packing design that was not included in the original data set, producing very promising results and thus demonstrating the potential that CFD and prediction correlations can have on the optimization of future structured packing designs. We are currently exploring the effects of the presence of a gap between the sheets and its effect on the pressure drop results under different flow conditions. Furthermore, it would be interesting to simulate the varied inclination angle and geometries over a larger domain to ensure that the flow characteristics and pressure drop results are observed, particularly when the flow behavior becomes more erratic.

Having the ability to predict pressure drop for different packing geometries can aid the optimization of future packing designs. Increasing the opening angle decreases the pressure drop as the channel walls separate further thus reducing wall friction. It is further decreased by increasing the channel height as the cross-sectional area of the channels increases producing a larger cavity for the gas to traverse. Moreover, faster velocities increase the Reynolds number making the flow unstable, thus further promoting the pressure drop. The ideal packing characteristics for minimizing the pressure drop, would be to increase the channel height and opening angle, thus increasing the cross-sectional area of the channel. The inclination angle results, shown in Figure 4, suggest that a high inclination angles, such as 60°, would further minimize the pressure drop. A simulation was carried out on a structured packing with an opening angle of 120°, channel height of 12 mm, and an inclination angle of 60°. The data of which were not included in the original data set for the generation of the correlation. The pressure drop information is compared with the predicted pressure drop in Figure 7. The simulated data for this geometric set up was not included in the data set used to produce the pressure drop correlation, yet the predicted pressure drops agree very well with the simulated data over a range of f-factors which is a promising indication that the correlations can be used to predict pressure drops to optimize structured packing geometries.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: s.gu@cranfield.ac.uk. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from the EPSRC project: Computational Modelling and Optimisation of Carbon Capture Reactors (Grant No. EP/J020184/1) and EU FP7 iComFluid project (312261).

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CONCLUSION Two dry pressure drop correlations were developed that considered the loss of pressure due to friction between structured packing sheets. A CFD simulation of Montz-Pak B1-250.45 packing was validated against experimental data, and the bulk pressure drop was attributed to the frictional losses. The first correlation demonstrated the impact the inclination angle has on the pressure drop, and that it needs to be considered as a separate factor, in addition to its impact on the effective gas velocity. The second correlation introduced the inclination angle factor to a previously published correlation that considered the effects of channel geometries alone,12 which greatly improved the pressure drop predictions for a range of simulated pressure drop data. The new correlation predicted

NOMENCLATURE

Greek Letters

a = inclination angle, deg ΔP = pressure drop, Pa Γi = constant μ = viscosity, kg/(s m) ω = specific dissipation rate of turbulent kinetic energy, m−2/ s−3 Ψ = fraction of channels ending at a wall ρ = density, kg/m3 Θi = constant υ = velocity, m/s ξdc = drag loss coefficient 4377



Research Note

ξf = frictional loss coefficient k = turbulent kinetic energy, m2/s2

(19) Forrester, A.; Sobester, S.; Keane, A. Engineering Design via Surrogate Modelling: A Practical Approach; Wiley-Blackwell: Hoboken, NJ, 2008.

Symbols

Ag = packing void fraction b = channel base, m Ci = loss coefficient parameters dc = column diameter, m g = acceleration due to gravity, m/s2 h = channel height, m hpe = packing element height, m p = pressure, Pa Re = Reynolds number t = time, s

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REFERENCES

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Dry Pressure Drop Prediction within Montz-pak B1-250.45 Packing

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