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Static mixers with a gas continuous phase
Chemical Engineering Science 61 (2006) 3429 – 3434 www.elsevier.com/locate/ces
Review
Static mixers with a gas continuous phase A. Couvert a, ∗ , C. Sanchez a , I. Charron b , A. Laplanche a , C. Renner b a LARCIP—ENSCR, Avenue du Général Leclerc, 35700 Rennes, France b ANJOU RECHERCHE—VEOLIA WATER, Chemin de la Digue, BP 76, 78603 Maisons-Laffitte, France
Received 13 May 2005; received in revised form 17 October 2005; accepted 17 November 2005 Available online 25 January 2006
Abstract The aim of this work was to characterise hydrodynamics and mass transfer in a gas–liquid contactor containing static mixers (SMs). The originality of this study lies in the fact that these mixing organs are used with a gas continuous phase. Two types of SM were implemented in co-current flows, Statiflo and Lightnin. The pressure drop P , the volumic interfacial area a and the volumic mass transfer coefficient kL a were measured in several configurations: horizontal flow, vertical up-flow and vertical down-flow. The influences of position and flow rates were studied in order to understand the behaviour of these contactors, and to optimise the operating conditions. As expected, the pressure drop was found to increase mainly with gas velocity but also with liquid velocity, and to reach 3300 Pa in the range of velocities studied (the gas flow rate varied between 4 and 30 m3 /h and the liquid flow rate between 0 and 100 L/h), far less than Sülzer SM. The volumic interfacial area and the volumic mass transfer coefficient showed the same changes, a varying between 100 and 1000 m2 /m3 , and kL a reaching 0.07 L/s. This is interesting compared with other classical absorption processes: indeed, even if packing towers can provide the same range of values, the operating conditions are more drastic or the dimensions of the apparatuses are far larger than SM ones. The position was also found to have an influence on the hydrodynamic and mass transfer parameters (P , a and kL a). 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Static mixers; Hydrodynamics; Mass transfer; Absorption; Environment; Gas treatment
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3430 2. Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3430 3. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.1. Pressure drop “P” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.1.1. Influence of the type of contactor, the gas and liquid flow rates, and the SM configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.1.2. Empirical two phase flow correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.1.3. Single phase flow study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.2. Volumic interfacial area “a” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.3. Volumic mass transfer coefficient “kL a” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3433 4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3434 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3434
∗ Corresponding author. Tel.: +33 (0)2 23 23 80 48; fax: +33 (0)2 23 23 81 20. E-mail address: [email protected] (A. Couvert).
0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.11.040
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A. Couvert et al. / Chemical Engineering Science 61 (2006) 3429 – 3434
1. Introduction Because of the diversity of the absorption apparatuses existing on the market (stirred tanks, bubble columns, packed-bed columns, plate columns, static and dynamic mixers), the choice for the best absorption technique (for odour removal for example) is not easy. The difficulty lies in the fact that a given process can be the most convenient or not efficient at all depending on the chemical operation realised. This depends on several parameters, such as physical and chemical properties of the present species, the temperature and pressure conditions, or the reaction kinetics. Streiff and Rogers (1994) wrote that a reactor must be designed for optimal conversion and selectivity. But the residence time must also be well chosen compared with the reaction kinetics. Besides, the cost factors should not be neglected, and so, the optimisation of such processes implies a hydrodynamic study (depending on the phase flow rates and the energy input). Finally, the process has to satisfy the time and space constraints. Up to now, many researchers have given their attention to static mixers (SMs) because of their numerous advantages: they are high energy systems, so that they can be excellent mixing processes, the investment and operating costs are low compared with a dynamic system, the residence time distribution is similar to a plug-flow, fluids are homogeneously dispersed in the reactor (Cybulski and Werner, 1986). Compared to classic mixing or mass transfer processes, they can be used at large gas and liquid flow rates, for fluids of high viscosity, and they do not need much maintenance. Zhu et al. (1992) wrote that SM enables the increase of reaction velocities and selectivity. As a consequence, SMs are largely used in industry: liquids or gas homogenisation, dispersion or emulsion with or without reaction in a gas–liquid system, but also heat and mass transfer operations like H2 S selective absorption in petroleum chemistry (Germain and Wetter, 1982). Nevertheless, it has also been shown that SMs generate a high pressure drop, which is strongly dependent on the geometry of the mixing elements (Pahl and Muschelknautz, 1982). The greater the space left for the fluid flow, the lower the pressure drop. Generally, SMs consist of iron or plastic elements placed in a tube. Their shape and size are various. Sülzer ones are embossed plates stacked in layers forming open channels, crossing by the disposition of two successive plates (90◦ deviation). Statiflo and Lightnin SMs are helical elements, allowing the fluids to rotate at 180◦ . Sometimes, an empty space is left between two mixing elements. Whereas the hydrodynamics and the gas–liquid mass transfer have been largely studied, most of the work has been conducted with a liquid continuous phase and a gaseous dispersed phase. Few studies have concerned SM with a gas continuous phase. Yet, Le Sauze et al. (1991), showed that SMs can be used to eliminate gaseous pollutants by transferring them in a liquid reactive phase, as packed towers do. In 1980, the Sülzer company designed a chemical scrubber, made of SMs, working in co-current flows. This contactor was implemented to remove acid gases like H2 S, HCl or SO2 with alkaline solutions, or basic gases like NH3 , alcohols or amines with acid solutions,
or even organic compounds. The scrubbing efficiency could be attributed to the exchange area (the interfacial area) existing between the gas and the liquid phases, which is all the more important that the droplets generated are small, for the chemical reaction coming into play. It could also be attributed to the great difference existing between the gas and liquid velocities (Roustan, 2003). The objective of this study was to characterise the performances of two types of SMs generating a low pressure drop, used with a gaseous continuous phase and a liquid dispersed phase. 2. Material and methods The SMs implemented in this study are Statiflo 100 and Lightnin 45 (Fig. 1). The contactor consists of six mixing elements of 4.4 cm length placed in a tube of 2.5 cm internal diameter and 25 cm length. The experimental set-up is shown in Fig. 2. Gas and liquid are introduced in co-current at superficial velocities ranging between 2 and 17 m/s for the gas (gas flow rate between 4 and 30 m3 /h) and between 0 and 0.06 m/s for the liquid (liquid flow rate between 0 and 100 L/h). Several configurations have been tested: horizontal flow (H), vertical up-flow (VU), and vertical down-flow (VD). The results were compared to those obtained in a previous study with Sülzer SMs (SMV4 -DN25), and to those obtained in an empty tube (ET). The pressure drop P was measured with manometers (tubes filled with water for the low pressure drops and with mercury for the high pressure drops). The volumic interfacial area a and the volumic mass transfer coefficient kL a were obtained by chemical methods. The irreversible chemical reaction of pseudofirst order between CO2 and NaOH 1 N led to a, whereas a physical absorption of gaseous acetaldehyde by water enabled to determine kL a. Fig. 2 presents the set-up realised for kL a assessment. The determination of a and kL a were performed with respect to the analyses realised on the inlet and the outlet gas phase. The CO2 concentration in the gas phase was measured with an IR analyser type BERYL 100 from COSMA, and the acetaldehyde concentration in the gas phase by HPLC with UV detection at 365 nm (C18 column, mobile phase composed of 75% methanol and 25% water), after bubbling in a 2,4-DNPH solution. a and kL a were deduced from Eqs. (2) and (3), obtained from the general mass transfer Eq. (1) and hypotheses on the reaction regime in the reactor. For the volumic interfacial area, E could be assumed to be equal to Ha (Hatta number), which is inversely proportional to kL , so that kL disappears from Eq. (1). For the volumic mass transfer coefficient, E is taken to be equal to 1, and then disappears from Eq. (1). ∗ − C ), N = kL aVE(CAL AL
a=
V
√
∗ DAL kC BL [(CAL,e
(1) N , ∗ ∗ /C ∗ − CAL,s )/(ln(CAL,e AL,s ))] (2)
A. Couvert et al. / Chemical Engineering Science 61 (2006) 3429 – 3434
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3. Results and discussion 3.1. Pressure drop “P” 3.1.1. Influence of the type of contactor, the gas and liquid flow rates, and the SM configuration The experiments carried out on the two types of SMs and in the ET show that the pressure drop increases mainly with the gas velocity and a little with the liquid velocity. Moreover, whatever the type of SM, the H and VD configurations generate similar pressure drops, whereas the VU configuration leads to far greater values. This can be explained by the fact that in the VU configuration, the liquid has to overcome the gravity force to flow out. To illustrate this phenomenon, Figs. 3 and 4 present the changes in pressure drops versus the gas velocity for the Lightnin and Statiflo SM in the three configurations (H, VD and VU) and for two liquid flow rates (QL = 27.5 and 97 L/h). Finally, whatever the flow direction, the pressure drops observed in the presence of both SMs are of the same order (1400–12 000 Pa/m or 100–3300 Pa). These values are much lower than those generated by Sülzer SM, which reach about 25 000 Pa in the same range of gas and liquid velocities (Couvert et al., 2002), but 10 times higher than those observed in the ET (10–320 Pa).
Fig. 1. Statiflo (left) and Lightnin (right) static mixers.
Gas
Tank Cs
Ce
Static mixers
Flow meter
Acetaldehyde
Gas-liquid separator
3.1.2. Empirical two phase flow correlation The pressure drop can be correlated by a power law type:
P = UG ;
Pump
Compressor
and vary with the configuration. For example, the values found for the Lightnin SM are reported in Table 1. Fig. 5 presents the fit between the experimental pressure drops measured for the Lightnin SM in position H and the empirical ones, calculated with Eq. (4).
Water
Fig. 2. Experimental set-up.
kL a =
(4)
3.1.3. Single phase flow study The SM study in single phase flow, that is when QL = 0 L/h, can be used to determine the Fanning factor f from the Darcy (5):
N , ∗ −(C ∗ −C ∗ /(C ∗ −C V [(CAL,e )/(ln CAL,e AL,s AL,s ))] AL,s AL,s
f= (3)
where N is the flux of product A transferred; V the liquid volume in the contactor; E the enhancement factor; DAL the diffusivity of the product A in the liquid used, D(CO2 )NaOH = 1.53 × 10−9 m2 /s (estimated with the relation proposed by Wilke and Chang, 1955); k the kinetic constant of the reaction between CO2 and NaOH 1 N, k=9340 L/(mol s) at T =20 ◦ C (estimated with the relation proposed by Laurent, 1975); CBL the NaOH liquid concentration; CAL,e and CAL,s the concentration of the ∗ product A in the liquid phase (inlet: e and outlet: s); CAL,e and ∗ CAL,s the concentration of the product A at the gas–liquid interface (inlet: e and outlet: s), calculated from the concentrations of the product A in the gas phase owing to Henry’s law and A the CO2 or acetaldehyde.
P D i , 2 2G nel Lel UG
(5)
where nel is the number of mixing elements (six in our study), Lel the length of a mixing element, G the gas density and Di the internal diameter of the tube. By identifying the experimental pressure drops for QL = 0 L/h to those calculated with the Darcy equation, the values found for the Fanning factor are reported in Table 2 for the Lightnin SM, the Statiflo SM and the ET. Note that Sülzer gives f = 1.85 for its SM, which suggests that the SMs chosen for this work consume far less energy. 3.2. Volumic interfacial area “a” The volumic interfacial area has been studied for both SM, the ET and in the H and VD configurations. Indeed, the VU
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3000
14000 12000
VD - QL = 97 L/h
2500
10000
H - QL = 27.5 L/h
2000
∆P=αUGβ
∆P/ L (Pa/m)
VD - QL = 27.5 L /h
H - QL = 97 L/h
8000
VU - QL = 27.5 L/h
6000
VU - QL = 97 L/h
+10% -10%
1500 1000
4000
500
2000
0 0
0 0
5
10
15
500
20
UG (m/s)
2500
3000
Fig. 3. Evolution of the pressure drop versus the gas velocity for the Lightnin static mixers in the three configurations (VD, H and VU) and for two liquid flow rates (QL = 27.5 and 97 L/h).
Fig. 5. Fitting between the empirical pressure drop (P = UG ) and the pressure drop measured in the Lightnin static mixers in the horizontal position.
Table 2 Values of the Fanning factor for the configurations H, VD and VU of the Lightnin SM, the Statiflo SM and the empty tube
14000 VD - QL = 27.5 L/h
∆P/L (Pa/m)
1000 1500 2000 ∆P measured
12000
VD - QL = 97 L/h
10000
H - QL = 27.5 L/h H - QL = 97 L/h
8000
VU - QL = 27.5 L/h
6000
VU - QL = 97 L/h
Horizontal (H) Vertical down-flow (VD) Vertical up-flow (VU)
fLIGHTNIN
fSTATIFLO
fEMPTY TUBE
0.25 0.28 0.29
0.39 0.40 0.39
0.022 0.021 0.023
4000 2000 800 0 5
10 UG (m/s)
15
20
Fig. 4. Evolution of the pressure drop versus the gas velocity for the Statiflo static mixers in the three configurations (VD, H and VU) and for two liquid flow rates (QL = 27.5 and 97 L/h).
600 a (m2/m3)
0
400 200 0
Table 1 and values for the configurations H, VD and VU of the Lightnin static mixers
Horizontal (H) Vertical down-flow (VD) Vertical up-flow (VU) a Values of
a
a
903UL + 7.3 105UL + 4.3 3059UL + 71.3
20–60 6–10 115–260
1.55 2.15 1.07
in the range of liquid velocities studied (for UL or QL = 0).
position is too difficult to implement because of the minima flow rates that must be kept in order to work in good conditions, so it has not been studied. For the other two configurations, H and VD, the results show that for whatever SM used, the volumic interfacial area increases with the gas and liquid flow rates. This can be explained by the increase in the number or the decrease of the size (if the number is constant) of the droplets formed when the fluid flows increase, improving the quality or the quantity of the dispersion. Figs. 6 and 7 present the evolution of the volumic interfacial area versus the ratio of mass liquid and gas flow rates L/G, for
0
2
4
6
L /G Lightnin
Statiflo
Empty tube
Fig. 6. Evolution of the volumic interfacial area in the different contactors versus the ratio L/G for the horizontal configuration (H) (QL = 69 L/h).
the different contactors, in the H and VD configurations when QL = 69 L/h. Whatever the type of SM, the VD position leads to volumic interfacial areas that are slightly higher than the H position (300.1000 m2 /m3 instead of 100.800 m2 /m3 ). This can be explained by the gravity force that plays a positive role in the VD position whereas it constitutes a brake to the liquid flow in position H. Moreover, it can be noticed that both SMs give approximately the same values of interfacial area. Finally, it should be noted that the values obtained with this type of contactor, SMs, are higher than those met in classical processes in which the gas is the continuous phase, like packed towers. Indeed, concerning conventional dumped packing, the geometric interfacial area is generally equal to about 300 m2 /m3 , and in the counter-current conditions (involving
A. Couvert et al. / Chemical Engineering Science 61 (2006) 3429 – 3434
0.07
1000
QL = 27.5 L/h
0.06
800
QL = 39 L/h
0.05 600
kLa (1/s)
a (m2/m3)
3433
400
QL = 52 L/h
0.04
QL = 69 L/h
0.03 0.02
200
0.01 0 0
2
Lightnin
4 L/G Statiflo
6
0.00
8
0
1
2
3
4
5
L /G Empty tube
Fig. 7. Evolution of the volumic interfacial area in the different contactors versus the ratio L/G for the configuration vertical down-flow (VD) (QL = 69 L/h).
Fig. 8. Evolution of the volumic mass transfer coefficient kL a versus the ratio L/G for the Lightnin SM—configuration VD.
0.08
QL = 27.5 L/h
3.3. Volumic mass transfer coefficient “kL a” Streiff et al. (1999) formulated the hypothesis that SMs generate a liquid film on the inner surface of the tube as well as fine droplets that are the “actors” of the mass transfer and the reaction. Given the fact that the VU position, even if it presents some advantages concerning turbulence and thus the interfacial area, generates a high pressure drop as an operating problem, and since the VD position leads to slightly higher interfacial areas than the position H, it is the VD position that has been retained to study the volumic mass transfer coefficient kL a. Changes in this parameter are shown in Figs. 8–10, for the different contactors in the VD position, versus the ratio L/G because of a smaller spread of the points. Even if it is not evident in these figures, it was shown that kL a increases with gas and liquid flow rates, as good as the volumic interfacial area. Promising values, up to 0.07 L/s, have been measured in these operating conditions, whatever the type of SM (Lightnin or Statiflo). As a comparison, kL a found in random packing towers vary between 4 × 10−4 and 0.06 L/s (Charpentier, 1981). The ones found in structured packing towers are expected to be higher. Nevertheless, it depends on the geometric characteristics of the
0.06
QL = 39 L/h QL = 52 L/h
0.05
QL = 69 L/h
0.04 0.03 0.02 0.01 0.00 0
1
2
3
4
5
L /G Fig. 9. Evolution of the volumic mass transfer coefficient kL a versus the ratio L/G for the Statiflo SM—configuration VD.
0.05 QL = 27.5 L /h
0.04 kLa (1/s)
low L/G operating ratios, about 1 to 3), the effective wet interfacial area rarely reaches the geometric value. In other words, with counter-current flow operation, the interfacial area values are lower than those obtained in SM. Nevertheless, some packing towers can operate with co-current flows, and structured packing, which offer geometric values of the interfacial area ranging from 250 up to 750 m2 /m3 . Raynal et al. (2004) used 410 m2 /m3 structured packing, and found that the effective wet interfacial area can reach the geometric value if the liquid velocity is sufficient, that is if the L/G ratio is sufficient (greater than 20). But this ratio is high in comparison with the common range for the absorption applications, and especially with the ratios implemented in this study. Note: the tube walls are not transparent, so that we could not observe breaking and coalescence phenomena; but it seems evident that these can influence the interfacial volumic area.
kLa (1/s)
0.07
QL = 39 L/h QL = 52 L/h
0.03
QL = 69 L/h
0.02 0.01 0.00 0
1
2
3
4
5
L /G
Fig. 10. Evolution of the volumic mass transfer coefficient kL a versus the ratio L/G for the empty tube (ET)—configuration VD.
packing elements. For example, Laurano and Paglianti (1999) found maximal kL a values of 0.01 L/s in columns filled with 1–4 inches diameter packing, whereas L/G ratios were high (far superior to 2 or 3). Besides, the kL a measured in the ET in the VD configuration have been found similar to those measured in the presence of SM at low liquid velocity but clearly lower than those when the liquid velocity is high. This confirms the idea that for high liquid velocities, SMs are of important interest for the dispersion of the liquid phase, whereas for low liquid velocities, the flow in the ET is sufficient.
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A. Couvert et al. / Chemical Engineering Science 61 (2006) 3429 – 3434
4. Conclusion Up to now, hydrodynamics and gas–liquid mass transfer in static mixers (SMs) have essentially been studied with a liquid continuous phase and a gas dispersed phase. The originality of this work lies in an inverse use of these contactors. Two types of SMs (Lightnin and Statiflo) have been implemented with a gas continuous phase. This study has shown that the Lightnin and Statiflo SMs are efficient and promising mass transfer organs, especially as acceptable pressure drops have been obtained in these contactors. Moreover, high values of the volumic interfacial area and interesting values of the volumic mass transfer coefficient have been measured, especially taking the operating conditions implemented and the size of the apparatuses into account. Few differences have been observed between the two types of SMs, certainly due to their similar geometrical design. The influence of the SM position on the performances of the contactor has also been demonstrated. The main conclusions that can be drawn are the following: the vertical up-flow position proved to be very efficient but constraining in terms of energy costs and operating conditions; at low flow rates, the horizontal position leads to a flow stratification, inappropriate for mixing and/or mass transfer when the fluid velocities are low; the vertical down-flow position seems to be the most convenient because it is easy to use, provides low pressure drops and good mass transfer coefficients. Notation a C C∗ CBL DAL Di E f G k kL kL a L Lel nel
volumic interfacial area, L−1 concentration in the liquid phase, in the bulk, N/L3 concentration at the gas–liquid interface, N/L3 NaOH liquid concentration, N/L3 diffusivity of the product A in the liquid used, L2 /T internal diameter of the tube, L enhancement factor friction factor mass gas flow rate per surface unit, M/L2 /T kinetic constant of the reaction between CO2 and NaOH 1 N, L3 /N/T liquid side mass transfer coefficient, L/T volumic liquid side mass transfer coefficient, T−1 mass liquid flow rate per surface unit M/L2 /T length of a mixing element, L number of mixing elements
N Q U V
flux of product A transferred, N/T flow rate, L3 /T superficial velocity, L/T liquid volume in the contactor, L3
Greek letters P
pressure drop, Pa density, M/L3
Indices i, e G, L
inlet, outlet gas, liquid
References Charpentier, J.-C., 1981. Mass transfer rates in gas liquid absorbers and reactors. In: Drew, T.B., Cokelet, G.R., Hoopes, J.W., Vermeulen, T. (Eds.), Advances in Chemical Engineering, vol. 11. Academic Press, New York, pp. 1133–1134. Couvert, A., Péculier, M.-F., Laplanche, A., 2002. Pressure drop and mass transfer study in static mixers with gas continuous phase. Canadian Journal Chemical Engineering 80 (4), 727–733. Cybulski, A., Werner, K., 1986. Static mixers—criteria for applications and selection. International Chemical Engineering 26 (1), 171–180. Germain, E., Wetter, R., 1982. Mélange statique de gaz. Informations Chimie 232, 135–139. Laurano, P.M., Paglianti, A., 1999. Performance of absorption columns equipped with low pressure drops structured packings. Industrial Engineering Chemistry Research 38, 3481–3488. Laurent, A., 1975. Etude de l’hydrodynamique et de transfert de matière dans une colonne à garnissage. Simulation de son fonctionnement à contrecourant par des modèles expérimentaux de laboratoire lors d’une absorption gaz-liquide avec réaction chimique. Thèse de doctorat d’état, INPL, Nancy, France. Le Sauze, N., Laplanche, A., Martin, G., Paillard, H., 1991. A process of washing and ozonation to deodorize an atmosphere contaminated by sulfides. Ozone Science and Engineering 13 (3), 331–347. Pahl, M.H., Muschelknautz, E., 1982. Static mixers and their applications. International Chemical Engineering 22 (2), 197–205. Raynal, L., Ballaguet, J.-P., Barrere-Tricca, C., 2004. Determination of mass transfer characteristics of co-current two-phase flow within structured packing. Chemical Engineering Science 59, 5395–5402. Roustan, M., 2003. Transferts gaz–liquide dans les procédés de traitement des eaux et des effluents gazeux. Tech. & Doc, Lavoisier, Paris. Streiff, F.A., Rogers, J.A., 1994. Don’t overlook static-mixer reactors. Chemical Engineering 101, 76–82. Streiff, F.A., Jaffer, S., Schenider, G., 1999. The design and application of static mixer technology. Third International Symposium on Mixing in Industrial Processes, Osaka, Japan. pp. 107–114. Wilke, C.R., Chang, P., 1955. Correlation of diffusion coefficients in dilute solution. A.I.Ch.E. Journal 1, 264–270. Zhu, Z.M., Hannon, J., Green, A., 1992. Use of high intensity gas–liquid mixers as reactors. Chemical Engineering Science 47 (9–11), 2847–2852.
Review
Static mixers with a gas continuous phase A. Couvert a, ∗ , C. Sanchez a , I. Charron b , A. Laplanche a , C. Renner b a LARCIP—ENSCR, Avenue du Général Leclerc, 35700 Rennes, France b ANJOU RECHERCHE—VEOLIA WATER, Chemin de la Digue, BP 76, 78603 Maisons-Laffitte, France
Received 13 May 2005; received in revised form 17 October 2005; accepted 17 November 2005 Available online 25 January 2006
Abstract The aim of this work was to characterise hydrodynamics and mass transfer in a gas–liquid contactor containing static mixers (SMs). The originality of this study lies in the fact that these mixing organs are used with a gas continuous phase. Two types of SM were implemented in co-current flows, Statiflo and Lightnin. The pressure drop P , the volumic interfacial area a and the volumic mass transfer coefficient kL a were measured in several configurations: horizontal flow, vertical up-flow and vertical down-flow. The influences of position and flow rates were studied in order to understand the behaviour of these contactors, and to optimise the operating conditions. As expected, the pressure drop was found to increase mainly with gas velocity but also with liquid velocity, and to reach 3300 Pa in the range of velocities studied (the gas flow rate varied between 4 and 30 m3 /h and the liquid flow rate between 0 and 100 L/h), far less than Sülzer SM. The volumic interfacial area and the volumic mass transfer coefficient showed the same changes, a varying between 100 and 1000 m2 /m3 , and kL a reaching 0.07 L/s. This is interesting compared with other classical absorption processes: indeed, even if packing towers can provide the same range of values, the operating conditions are more drastic or the dimensions of the apparatuses are far larger than SM ones. The position was also found to have an influence on the hydrodynamic and mass transfer parameters (P , a and kL a). 䉷 2005 Elsevier Ltd. All rights reserved. Keywords: Static mixers; Hydrodynamics; Mass transfer; Absorption; Environment; Gas treatment
Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3430 2. Material and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3430 3. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.1. Pressure drop “P” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.1.1. Influence of the type of contactor, the gas and liquid flow rates, and the SM configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.1.2. Empirical two phase flow correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.1.3. Single phase flow study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.2. Volumic interfacial area “a” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 3.3. Volumic mass transfer coefficient “kL a” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3433 4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3434 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3434
∗ Corresponding author. Tel.: +33 (0)2 23 23 80 48; fax: +33 (0)2 23 23 81 20. E-mail address: [email protected] (A. Couvert).
0009-2509/$ - see front matter 䉷 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2005.11.040
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1. Introduction Because of the diversity of the absorption apparatuses existing on the market (stirred tanks, bubble columns, packed-bed columns, plate columns, static and dynamic mixers), the choice for the best absorption technique (for odour removal for example) is not easy. The difficulty lies in the fact that a given process can be the most convenient or not efficient at all depending on the chemical operation realised. This depends on several parameters, such as physical and chemical properties of the present species, the temperature and pressure conditions, or the reaction kinetics. Streiff and Rogers (1994) wrote that a reactor must be designed for optimal conversion and selectivity. But the residence time must also be well chosen compared with the reaction kinetics. Besides, the cost factors should not be neglected, and so, the optimisation of such processes implies a hydrodynamic study (depending on the phase flow rates and the energy input). Finally, the process has to satisfy the time and space constraints. Up to now, many researchers have given their attention to static mixers (SMs) because of their numerous advantages: they are high energy systems, so that they can be excellent mixing processes, the investment and operating costs are low compared with a dynamic system, the residence time distribution is similar to a plug-flow, fluids are homogeneously dispersed in the reactor (Cybulski and Werner, 1986). Compared to classic mixing or mass transfer processes, they can be used at large gas and liquid flow rates, for fluids of high viscosity, and they do not need much maintenance. Zhu et al. (1992) wrote that SM enables the increase of reaction velocities and selectivity. As a consequence, SMs are largely used in industry: liquids or gas homogenisation, dispersion or emulsion with or without reaction in a gas–liquid system, but also heat and mass transfer operations like H2 S selective absorption in petroleum chemistry (Germain and Wetter, 1982). Nevertheless, it has also been shown that SMs generate a high pressure drop, which is strongly dependent on the geometry of the mixing elements (Pahl and Muschelknautz, 1982). The greater the space left for the fluid flow, the lower the pressure drop. Generally, SMs consist of iron or plastic elements placed in a tube. Their shape and size are various. Sülzer ones are embossed plates stacked in layers forming open channels, crossing by the disposition of two successive plates (90◦ deviation). Statiflo and Lightnin SMs are helical elements, allowing the fluids to rotate at 180◦ . Sometimes, an empty space is left between two mixing elements. Whereas the hydrodynamics and the gas–liquid mass transfer have been largely studied, most of the work has been conducted with a liquid continuous phase and a gaseous dispersed phase. Few studies have concerned SM with a gas continuous phase. Yet, Le Sauze et al. (1991), showed that SMs can be used to eliminate gaseous pollutants by transferring them in a liquid reactive phase, as packed towers do. In 1980, the Sülzer company designed a chemical scrubber, made of SMs, working in co-current flows. This contactor was implemented to remove acid gases like H2 S, HCl or SO2 with alkaline solutions, or basic gases like NH3 , alcohols or amines with acid solutions,
or even organic compounds. The scrubbing efficiency could be attributed to the exchange area (the interfacial area) existing between the gas and the liquid phases, which is all the more important that the droplets generated are small, for the chemical reaction coming into play. It could also be attributed to the great difference existing between the gas and liquid velocities (Roustan, 2003). The objective of this study was to characterise the performances of two types of SMs generating a low pressure drop, used with a gaseous continuous phase and a liquid dispersed phase. 2. Material and methods The SMs implemented in this study are Statiflo 100 and Lightnin 45 (Fig. 1). The contactor consists of six mixing elements of 4.4 cm length placed in a tube of 2.5 cm internal diameter and 25 cm length. The experimental set-up is shown in Fig. 2. Gas and liquid are introduced in co-current at superficial velocities ranging between 2 and 17 m/s for the gas (gas flow rate between 4 and 30 m3 /h) and between 0 and 0.06 m/s for the liquid (liquid flow rate between 0 and 100 L/h). Several configurations have been tested: horizontal flow (H), vertical up-flow (VU), and vertical down-flow (VD). The results were compared to those obtained in a previous study with Sülzer SMs (SMV4 -DN25), and to those obtained in an empty tube (ET). The pressure drop P was measured with manometers (tubes filled with water for the low pressure drops and with mercury for the high pressure drops). The volumic interfacial area a and the volumic mass transfer coefficient kL a were obtained by chemical methods. The irreversible chemical reaction of pseudofirst order between CO2 and NaOH 1 N led to a, whereas a physical absorption of gaseous acetaldehyde by water enabled to determine kL a. Fig. 2 presents the set-up realised for kL a assessment. The determination of a and kL a were performed with respect to the analyses realised on the inlet and the outlet gas phase. The CO2 concentration in the gas phase was measured with an IR analyser type BERYL 100 from COSMA, and the acetaldehyde concentration in the gas phase by HPLC with UV detection at 365 nm (C18 column, mobile phase composed of 75% methanol and 25% water), after bubbling in a 2,4-DNPH solution. a and kL a were deduced from Eqs. (2) and (3), obtained from the general mass transfer Eq. (1) and hypotheses on the reaction regime in the reactor. For the volumic interfacial area, E could be assumed to be equal to Ha (Hatta number), which is inversely proportional to kL , so that kL disappears from Eq. (1). For the volumic mass transfer coefficient, E is taken to be equal to 1, and then disappears from Eq. (1). ∗ − C ), N = kL aVE(CAL AL
a=
V
√
∗ DAL kC BL [(CAL,e
(1) N , ∗ ∗ /C ∗ − CAL,s )/(ln(CAL,e AL,s ))] (2)
A. Couvert et al. / Chemical Engineering Science 61 (2006) 3429 – 3434
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3. Results and discussion 3.1. Pressure drop “P” 3.1.1. Influence of the type of contactor, the gas and liquid flow rates, and the SM configuration The experiments carried out on the two types of SMs and in the ET show that the pressure drop increases mainly with the gas velocity and a little with the liquid velocity. Moreover, whatever the type of SM, the H and VD configurations generate similar pressure drops, whereas the VU configuration leads to far greater values. This can be explained by the fact that in the VU configuration, the liquid has to overcome the gravity force to flow out. To illustrate this phenomenon, Figs. 3 and 4 present the changes in pressure drops versus the gas velocity for the Lightnin and Statiflo SM in the three configurations (H, VD and VU) and for two liquid flow rates (QL = 27.5 and 97 L/h). Finally, whatever the flow direction, the pressure drops observed in the presence of both SMs are of the same order (1400–12 000 Pa/m or 100–3300 Pa). These values are much lower than those generated by Sülzer SM, which reach about 25 000 Pa in the same range of gas and liquid velocities (Couvert et al., 2002), but 10 times higher than those observed in the ET (10–320 Pa).
Fig. 1. Statiflo (left) and Lightnin (right) static mixers.
Gas
Tank Cs
Ce
Static mixers
Flow meter
Acetaldehyde
Gas-liquid separator
3.1.2. Empirical two phase flow correlation The pressure drop can be correlated by a power law type:
P = UG ;
Pump
Compressor
and vary with the configuration. For example, the values found for the Lightnin SM are reported in Table 1. Fig. 5 presents the fit between the experimental pressure drops measured for the Lightnin SM in position H and the empirical ones, calculated with Eq. (4).
Water
Fig. 2. Experimental set-up.
kL a =
(4)
3.1.3. Single phase flow study The SM study in single phase flow, that is when QL = 0 L/h, can be used to determine the Fanning factor f from the Darcy (5):
N , ∗ −(C ∗ −C ∗ /(C ∗ −C V [(CAL,e )/(ln CAL,e AL,s AL,s ))] AL,s AL,s
f= (3)
where N is the flux of product A transferred; V the liquid volume in the contactor; E the enhancement factor; DAL the diffusivity of the product A in the liquid used, D(CO2 )NaOH = 1.53 × 10−9 m2 /s (estimated with the relation proposed by Wilke and Chang, 1955); k the kinetic constant of the reaction between CO2 and NaOH 1 N, k=9340 L/(mol s) at T =20 ◦ C (estimated with the relation proposed by Laurent, 1975); CBL the NaOH liquid concentration; CAL,e and CAL,s the concentration of the ∗ product A in the liquid phase (inlet: e and outlet: s); CAL,e and ∗ CAL,s the concentration of the product A at the gas–liquid interface (inlet: e and outlet: s), calculated from the concentrations of the product A in the gas phase owing to Henry’s law and A the CO2 or acetaldehyde.
P D i , 2 2G nel Lel UG
(5)
where nel is the number of mixing elements (six in our study), Lel the length of a mixing element, G the gas density and Di the internal diameter of the tube. By identifying the experimental pressure drops for QL = 0 L/h to those calculated with the Darcy equation, the values found for the Fanning factor are reported in Table 2 for the Lightnin SM, the Statiflo SM and the ET. Note that Sülzer gives f = 1.85 for its SM, which suggests that the SMs chosen for this work consume far less energy. 3.2. Volumic interfacial area “a” The volumic interfacial area has been studied for both SM, the ET and in the H and VD configurations. Indeed, the VU
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3000
14000 12000
VD - QL = 97 L/h
2500
10000
H - QL = 27.5 L/h
2000
∆P=αUGβ
∆P/ L (Pa/m)
VD - QL = 27.5 L /h
H - QL = 97 L/h
8000
VU - QL = 27.5 L/h
6000
VU - QL = 97 L/h
+10% -10%
1500 1000
4000
500
2000
0 0
0 0
5
10
15
500
20
UG (m/s)
2500
3000
Fig. 3. Evolution of the pressure drop versus the gas velocity for the Lightnin static mixers in the three configurations (VD, H and VU) and for two liquid flow rates (QL = 27.5 and 97 L/h).
Fig. 5. Fitting between the empirical pressure drop (P = UG ) and the pressure drop measured in the Lightnin static mixers in the horizontal position.
Table 2 Values of the Fanning factor for the configurations H, VD and VU of the Lightnin SM, the Statiflo SM and the empty tube
14000 VD - QL = 27.5 L/h
∆P/L (Pa/m)
1000 1500 2000 ∆P measured
12000
VD - QL = 97 L/h
10000
H - QL = 27.5 L/h H - QL = 97 L/h
8000
VU - QL = 27.5 L/h
6000
VU - QL = 97 L/h
Horizontal (H) Vertical down-flow (VD) Vertical up-flow (VU)
fLIGHTNIN
fSTATIFLO
fEMPTY TUBE
0.25 0.28 0.29
0.39 0.40 0.39
0.022 0.021 0.023
4000 2000 800 0 5
10 UG (m/s)
15
20
Fig. 4. Evolution of the pressure drop versus the gas velocity for the Statiflo static mixers in the three configurations (VD, H and VU) and for two liquid flow rates (QL = 27.5 and 97 L/h).
600 a (m2/m3)
0
400 200 0
Table 1 and values for the configurations H, VD and VU of the Lightnin static mixers
Horizontal (H) Vertical down-flow (VD) Vertical up-flow (VU) a Values of
a
a
903UL + 7.3 105UL + 4.3 3059UL + 71.3
20–60 6–10 115–260
1.55 2.15 1.07
in the range of liquid velocities studied (for UL or QL = 0).
position is too difficult to implement because of the minima flow rates that must be kept in order to work in good conditions, so it has not been studied. For the other two configurations, H and VD, the results show that for whatever SM used, the volumic interfacial area increases with the gas and liquid flow rates. This can be explained by the increase in the number or the decrease of the size (if the number is constant) of the droplets formed when the fluid flows increase, improving the quality or the quantity of the dispersion. Figs. 6 and 7 present the evolution of the volumic interfacial area versus the ratio of mass liquid and gas flow rates L/G, for
0
2
4
6
L /G Lightnin
Statiflo
Empty tube
Fig. 6. Evolution of the volumic interfacial area in the different contactors versus the ratio L/G for the horizontal configuration (H) (QL = 69 L/h).
the different contactors, in the H and VD configurations when QL = 69 L/h. Whatever the type of SM, the VD position leads to volumic interfacial areas that are slightly higher than the H position (300.1000 m2 /m3 instead of 100.800 m2 /m3 ). This can be explained by the gravity force that plays a positive role in the VD position whereas it constitutes a brake to the liquid flow in position H. Moreover, it can be noticed that both SMs give approximately the same values of interfacial area. Finally, it should be noted that the values obtained with this type of contactor, SMs, are higher than those met in classical processes in which the gas is the continuous phase, like packed towers. Indeed, concerning conventional dumped packing, the geometric interfacial area is generally equal to about 300 m2 /m3 , and in the counter-current conditions (involving
A. Couvert et al. / Chemical Engineering Science 61 (2006) 3429 – 3434
0.07
1000
QL = 27.5 L/h
0.06
800
QL = 39 L/h
0.05 600
kLa (1/s)
a (m2/m3)
3433
400
QL = 52 L/h
0.04
QL = 69 L/h
0.03 0.02
200
0.01 0 0
2
Lightnin
4 L/G Statiflo
6
0.00
8
0
1
2
3
4
5
L /G Empty tube
Fig. 7. Evolution of the volumic interfacial area in the different contactors versus the ratio L/G for the configuration vertical down-flow (VD) (QL = 69 L/h).
Fig. 8. Evolution of the volumic mass transfer coefficient kL a versus the ratio L/G for the Lightnin SM—configuration VD.
0.08
QL = 27.5 L/h
3.3. Volumic mass transfer coefficient “kL a” Streiff et al. (1999) formulated the hypothesis that SMs generate a liquid film on the inner surface of the tube as well as fine droplets that are the “actors” of the mass transfer and the reaction. Given the fact that the VU position, even if it presents some advantages concerning turbulence and thus the interfacial area, generates a high pressure drop as an operating problem, and since the VD position leads to slightly higher interfacial areas than the position H, it is the VD position that has been retained to study the volumic mass transfer coefficient kL a. Changes in this parameter are shown in Figs. 8–10, for the different contactors in the VD position, versus the ratio L/G because of a smaller spread of the points. Even if it is not evident in these figures, it was shown that kL a increases with gas and liquid flow rates, as good as the volumic interfacial area. Promising values, up to 0.07 L/s, have been measured in these operating conditions, whatever the type of SM (Lightnin or Statiflo). As a comparison, kL a found in random packing towers vary between 4 × 10−4 and 0.06 L/s (Charpentier, 1981). The ones found in structured packing towers are expected to be higher. Nevertheless, it depends on the geometric characteristics of the
0.06
QL = 39 L/h QL = 52 L/h
0.05
QL = 69 L/h
0.04 0.03 0.02 0.01 0.00 0
1
2
3
4
5
L /G Fig. 9. Evolution of the volumic mass transfer coefficient kL a versus the ratio L/G for the Statiflo SM—configuration VD.
0.05 QL = 27.5 L /h
0.04 kLa (1/s)
low L/G operating ratios, about 1 to 3), the effective wet interfacial area rarely reaches the geometric value. In other words, with counter-current flow operation, the interfacial area values are lower than those obtained in SM. Nevertheless, some packing towers can operate with co-current flows, and structured packing, which offer geometric values of the interfacial area ranging from 250 up to 750 m2 /m3 . Raynal et al. (2004) used 410 m2 /m3 structured packing, and found that the effective wet interfacial area can reach the geometric value if the liquid velocity is sufficient, that is if the L/G ratio is sufficient (greater than 20). But this ratio is high in comparison with the common range for the absorption applications, and especially with the ratios implemented in this study. Note: the tube walls are not transparent, so that we could not observe breaking and coalescence phenomena; but it seems evident that these can influence the interfacial volumic area.
kLa (1/s)
0.07
QL = 39 L/h QL = 52 L/h
0.03
QL = 69 L/h
0.02 0.01 0.00 0
1
2
3
4
5
L /G
Fig. 10. Evolution of the volumic mass transfer coefficient kL a versus the ratio L/G for the empty tube (ET)—configuration VD.
packing elements. For example, Laurano and Paglianti (1999) found maximal kL a values of 0.01 L/s in columns filled with 1–4 inches diameter packing, whereas L/G ratios were high (far superior to 2 or 3). Besides, the kL a measured in the ET in the VD configuration have been found similar to those measured in the presence of SM at low liquid velocity but clearly lower than those when the liquid velocity is high. This confirms the idea that for high liquid velocities, SMs are of important interest for the dispersion of the liquid phase, whereas for low liquid velocities, the flow in the ET is sufficient.
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A. Couvert et al. / Chemical Engineering Science 61 (2006) 3429 – 3434
4. Conclusion Up to now, hydrodynamics and gas–liquid mass transfer in static mixers (SMs) have essentially been studied with a liquid continuous phase and a gas dispersed phase. The originality of this work lies in an inverse use of these contactors. Two types of SMs (Lightnin and Statiflo) have been implemented with a gas continuous phase. This study has shown that the Lightnin and Statiflo SMs are efficient and promising mass transfer organs, especially as acceptable pressure drops have been obtained in these contactors. Moreover, high values of the volumic interfacial area and interesting values of the volumic mass transfer coefficient have been measured, especially taking the operating conditions implemented and the size of the apparatuses into account. Few differences have been observed between the two types of SMs, certainly due to their similar geometrical design. The influence of the SM position on the performances of the contactor has also been demonstrated. The main conclusions that can be drawn are the following: the vertical up-flow position proved to be very efficient but constraining in terms of energy costs and operating conditions; at low flow rates, the horizontal position leads to a flow stratification, inappropriate for mixing and/or mass transfer when the fluid velocities are low; the vertical down-flow position seems to be the most convenient because it is easy to use, provides low pressure drops and good mass transfer coefficients. Notation a C C∗ CBL DAL Di E f G k kL kL a L Lel nel
volumic interfacial area, L−1 concentration in the liquid phase, in the bulk, N/L3 concentration at the gas–liquid interface, N/L3 NaOH liquid concentration, N/L3 diffusivity of the product A in the liquid used, L2 /T internal diameter of the tube, L enhancement factor friction factor mass gas flow rate per surface unit, M/L2 /T kinetic constant of the reaction between CO2 and NaOH 1 N, L3 /N/T liquid side mass transfer coefficient, L/T volumic liquid side mass transfer coefficient, T−1 mass liquid flow rate per surface unit M/L2 /T length of a mixing element, L number of mixing elements
N Q U V
flux of product A transferred, N/T flow rate, L3 /T superficial velocity, L/T liquid volume in the contactor, L3
Greek letters P
pressure drop, Pa density, M/L3
Indices i, e G, L
inlet, outlet gas, liquid
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