Design aspect of a novel L-shaped pulsed column for liquid–liquid extraction applications:Energy consumption and the characteristics velocity concept

Pouria Amani*,Elham Mohammadi,Sahar Akhgar

1 School of Chemical Engineering,College of Engineering,University of Tehran,P.O.Box:11155-4563,Tehran,Iran

2 Chemical Engineering Department,Tarbiat Modares University,P.O.Box:14115-143,Tehran,Iran

1.Introduction

Solvent extraction is one of the methods applied in separation industry.There are numerous types of extractors including mixersettlers,columns and centrifugal extractors[1].Pulsed columns are a class of solvent extractors which offer various advantages such as high throughput,simple design,low space requirement and no internal moving parts[2].

Various internals have been used so far in pulsed columns such as packing,perforated plates and disc&doughnuts.However,generally pulsed columns can be classi fied in two structural groups:1—vertical pulsed columns;2—horizontal pulsed columns.In most studies,vertical pulsed columns have been employed and investigated[3–5].However,in various applications,especially when height limitation is a concern or in nuclear industries it is highly required to use the horizontal pulsed columns[6–10].It should be noted that the mass transfer rate in verticaland horizontalstructure ofthe columns is approximately comparable[11]and the horizontal columns provide higher performance based on the identical required space,while the throughput of the horizontal columns is much less than the vertical ones.Therefore,there is a need to propose a new type of extraction columns which offers higher performance compared to previous conventionaltypes.In this regard,the novel L-shaped(horizontal–vertical)pulsed sieve-plate column has been proposed in order to potentially achieve higher advantages compared to the other types.In our previous studies,we have investigated the hydrodynamic of such columns and the results revealed that an L-shaped extraction column has a great potential to extract rare earth elements[12,13].However,the knowledge concerning the design and performance of such columns is still far from ful filling expectations due to the complex behaviors of the hydrodynamics as well as mass transfer performance.

One ofthe key factors in design and scale-up ofextraction columns is the total energy consumed during the steady-state operation of the apparatus.Among the various types of extraction columns,the L-shaped pulsed sieve-plate column is one type of extractors whose energy consumption is much less than that of the conventional vertical pulsed extraction columns with identical length,while their application for extraction,separation and puri fication of rare earth elements has not extensively been referred to the literature.Thus,the primary objective of this research is to study the feasibility of the L-shaped pulsed sieveplate columns for solventextraction applications by evaluating the consumption of energy at different conditions.

On the other hand,the characteristic velocity is another key factor in steady state operation of extraction columns since it demonstrates the maximum throughput of the column.The characteristic velocity can be obtained by flooding measurements,reported in our previous research for an L-shaped extraction column[13].Thus,this article also concerns the characteristic velocity approaches in order to evaluate the applicability of such models for an L-shaped extraction column.

2.Experimental

2.1.Description of equipment

Schematic diagram ofthe L-shaped pulsed sieve-plate column used in this work is illustrated in Fig.1.The setup consists ofverticaland horizontal parts,upper and lower settler,four tanks,two dosing pumps,two rotameters and air pulsating system.The active part of the column is a pipe housing an internal plate cartridge consisting of 24 pairs of sieve plate in the horizontal section as well as 29 individual sieve plates in the vertical section.The main characteristics of the column are listed in Table 1.

2.2.Liquid–liquid system

Liquid–liquid systems used in this work are toluene/water,butanol/water,butyl acetate/water in order to cover a wide range of interfacial tension.These systems have been recommended by the EuropeanFederation of Chemical Engineering as of ficial test systems for extraction investigations[14].The physical properties of these systems are listed in Table 2.All experiments are carried out at the(20 ± 1)°C.The density and viscosity of each phase are determined using a balance in the order of 0.0001 g and with a LAUDA viscometer.

Table 1 Plate properties

Fig.1.A schematic of the apparatus.

Table 2 Physical properties of the chemical systems at(20 ± 1)°C

2.3.Theoretical framework

2.3.1.Energy consumption concept

The pressure drop can be calculated by following classical Eq.(15):

where U represents the velocity,Dcis the column diameter,Z represents the distance between measuring points,ρmis the density ofthe mixture[Eq.(2)],and Δl represents the differential manometer height.In addition,C corresponds to the pressure drop coefficient in the case of permanent flow.

The velocity ofthe pulsed flow provided by an airpulsing system can be expressed in every moment as follows:

where A and f represent pulsation amplitude and frequency,and t represents time.The period of pulsation is T=1/f.So,the expression for U(t)(Eq.(3))can be rewritten as,

The energy is consumed by the flow with both positive and negative velocity.If integrated directly over the interval 0 to T,the mean velocity will be zero,because for the half of the interval the velocity is equal to the other half,but with opposite sign.For this reason,the absolute value of the velocity is integrated.To obtain the value of mean velocity,the period of pulsation can be divided in three zones:

(1)Time interval 0 to T/4—the velocity is positive.

(2)Time interval T/4 to 3/4 T-velocity is negative and its absolute value is taken.

(3)Time interval 3/4 T to T—the velocity is positive.It is analogous to the first zone and the result is the same.

Thus,the mean pulsation velocity(Um)can be expressed as follows:

Assuming that the pressure drop in a pulsed flow is proportional to the square of its velocity,one can replace the velocity term in Eq.(1)by the expression for mean pulsation velocity[Eq.(8)].This assumption is explicitly supported by the experimentalobservation ofother authors[16,17],stating that in both permanent and pulsed flows the energy(which is proportional to the product of pressure drop and velocity)is proportional to the cube of velocity.

Integration over a pulsation period T results in:

where C is a proportionality coefficientin case ofpermanent flow,Cpis for the case of a pulsed flow(2Af)is mean velocity of the pulsed flow.It is seen that the pressure drop coefficient for the pulsed flow Cpis about 25%greater than that of an equivalent permanent flow C.The pressure drop characterizes the column resistance.Energy is consumed to overcome this resistance so as to make the flow passing through the column.Arelation for determination ofenergy consumption due to pressure drop in an L-shaped extraction column with pulsed flow is developed below.In the case of a permanent flow,the force exerted perpendicular to the cross section of the column(FN)can be calculated by Eq.(11):

Therefore,the energy(E)consumed can be expressed as,

Replacing Δp in Eq.(12)by Eq.(1)results in:

Considering SX=V and Vρ=m,the energy consumption can be expressed by:

Consequently,since t=X/U,energy per unity of mass and time can be expressed as below:

Determining Δl from Eq.(1)can be resulted in Eq.(16).

For a pulsed flow,the consumption of energy and velocity vary regarding the time and depend on its moment during the pulsation.Thus,integrating overa period of pulsation can be resulted in the determination of the mean energy consumption,as follows:

The comparison of Eqs.(16)and(18)demonstrates that the mean energy consumed for a pulsed flow is one and a half times more than that of a permanent flow at identical velocity.

The mean energy consumption for a permanent flow can therefore be determined as below:

2.3.2.Characteristic velocity concept

With respect to the variation of pressure drop through the column length[13], flooding velocities can be determined.Consequently,the characteristic velocity can be obtained by flooding measurements.Many correlations are proposed for prediction of characteristic velocity in order to relate the slip velocity and the dispersed phase holdup.Thornton and Pratt[18]proposed a model for determination of U0at the flooding point as follows:

Thornton and Pratt[18]suggested that flooding will occur when the phases velocity reaches its highest value due to the variation of holdup.Therefore,for determination of flooding capacity in terms of dispersed and continuous phase velocities,Eq.(21)is differentiated based on φ,treating Udand Ucas dependent variables as follows:

Highest super ficial velocity of each phase can be determined by only one of Eq.(22)or(23)and by the other characteristic velocity approaches.With the substitution of Eq.(21)in Eqs.(22)and(23),the super ficial velocities at flooding point can be calculated as follows:

Another equation developed by Richardson and Zaki[19]which was originally presented for sedimenting and fluidized processes of homogenous solid particles.However,Godfrey and Slater[20]revealed that it has a wide applicability for determination of U0and also can be employed for liquid–liquid systems as follows:

where n is the parameter which has to be obtained based on the experimental data.It should be noted that the idea of differentiating the relationship between slip velocity and holdup to obtain limiting values of super ficial velocities(Udfand Ucf)was firstly presented by Dell and Pratt[21].In this approach,it is assumed that near the highest feasible flow rate,slight variation of one flow when the other is considered to be fixed,will significantly increase the holdup.Accordingly,Eq.(22)is differentiated based on φ,treating Udand Ucas dependent variables in order to determine flooding conditions,and the substitution of Eq.(26)in Eqs.(22)and(23)leads to:

3.Results and Discussion

3.1.Pressure drop

The primary objective of this research is to find how the pressure drop will change when varying the geometry parameters of the stage and pulsation parameters.In this regard,two dimensionless parameters characterize the stage geometry:plate free area(F)and dimensionless interplate distance(h)which is the ratio of the plate spacing to the column dimeter.The two-phase pressure drop through the column length is measured by using a manometer as can be seen in Fig.1.Each experiment is repeated three times to guarantee the statistical significance of the determined pressure drop.

To illustrate the in fluence of column geometry on pressure drop,the pulsed flow pressure drop coefficient(Cp)is studied at different plate distances and several constant values of plate free cross area.The Cpcan be generally obtained from experimentalΔp,Dc,ρ,X,and Af by plotting DcΔp/ρX versus(2Af)2.A linear plot through the origin between DcΔp/ρX versus(2Af)2can be observed which is in agreement with the general Eqs.(9)and(10).The slope of the lines corresponds to the pulsed flow pressure drop coefficient Cp.It is found that it does not depend on flow velocity and takes specific values for each particular stage configuration and extraction system.So,Cpcharacterizes the in fluence ofstage geometry.In this regard,Fig.2 exhibits the variation of Cpatdifferent h and F.

Accordingly,a numerically obtained relation for determination of pressure drop in the L-shaped pulsed sieve-plate extraction column is derived as below:

where K1=4.507,3.759,and 2.820 for toluene-water,butyl acetate–water and butanol–water,respectively.The Average Absolute Relative Error(AARE)is adopted to make comparison between the experimental data and the predicted results:

The AARE values between the experimentaldata and those obtained from Eq.(29)are about 9.48%,8.47%and 10.16%for toluene–water,butyl acetate–water and butanol–water,respectively.Also,an easy access to Emat different stage configurations is possible through Eq.(29)for determination of Cpor by an expression for CpEderived by combining Eqs.(29)and(19),as follows:

Fig.2.In fluence of interplate distance and plate free area on pressure drop coefficient.

where K2=6.009,5.012,and 3.760 for toluene-water,butyl acetate–water and butanol–water,respectively.As it is seen,the pulsed flow pressure drop coefficient Cpde fined by Eq.(29),does not depend on Re number.From one pointof view,Cpshould depend on Re number,since itintegrates the in fluence oftwo types ofhydraulic losses:Re dependent friction losses( flow in pipe)and Re independent local resistance losses( flow through ori fices).However,a possible explanation can be found by considering separately the in fluence of hydraulic losses.Calculations of local resistance and friction losses have revealed that the pressure drop due to friction is below 2%oftotalpressure drop,i.e.the localresistance losses in the studied column strongly dominate[13].In such a case,in view of the correlation precision of about 10%,negligible impact of Re number on Cpmight be expected.Additionally,in previous studies concerning one-phase flow in perforated plate columns with immobile or oscillating plates,no in fluence of Re on pressure drop have been observed[15,22,23].

3.2.Energy consumption in a pulsed flow

The secondary objective of this study was to investigate the energy input consumed for a steady state operating of a horizontal pulsed perforated-plate extraction column.Regarding to de fine the dynamic conditions ofthe column,the mean pulsed velocity has been considered using the Reynolds number:

where is the mixture kinematic viscosity.The mean energy consumption ofa pulsed two-phase flow versus various Reynolds numberis illustrated in Fig.3 forfour differentchemicalsystems.The calculated results are obtained through Eqs.(18)and(31)for the same conditions.The experimental observations reveal that when the Reynolds number is increased(higher pulsation intensity),the energy consumption is increased.It is because of the fact that when the pulsation intensity increments,the pressure drop along the column slightly increases which results in an increase in consumption of energy.Moreover,it is observed that,except for the kerosene-water system,the energy consumption decreases with an increase in the interfacialtension in different chemical systems.However,because of the significant difference between the other physical properties including density and viscosity of kerosene with other chemical liquids,different trend is observed in similar conditions for the kerosene-water system.

Fig.3.Mean energy consumption at various Reynolds numbers.

In order to provide a better evaluation of the energy consumption of an extraction column,the in fluence of geometrical parameters including the plate spacing and the plate free area is also investigated.In this regard,for evaluation of the plate spacing,the dimensionless interplate distance(H),which can be characterized as the ratio of the plate spacing to the column dimeter,is considered and the results for four different interplate distances(geometry ratio=H/Dc)are illustrated in Fig.4.It is observed that increasing the plate spacing leads to the reduction of energy consumption.Moreover,one can see that its influence becomes smaller at larger interplate distances and for greater values of h,the in fluence of plate spacing is not pronounced.According to the experimental results,with further increase in the geometry ratio,more than 1.5,the in fluence of increasing its value becomes insigni ficant.Thus,a value of h around 1.5 can be considered as the optimum values from the energy point of view.However,it should be noted that the geometry ratio also significantly affects the turbulence of the flow and consequently highly affects the mass transfer performance and a multi-objective optimization is required to evaluate the optimal condition of the column.

Fig.4.In fluence ofgeometry ratio h on energy consumption fordifferentchemicalsystems at Re=1.5 and F=0.11.

Furthermore,another affecting geometrical parameter called plate free area is also concerned.In this regard,three different internals(half-perforated plates)with 0.11,0.22,and 0.31 fractional free area are used,while the plate spacing is considered to be constant(0.06 m).The results for four different chemical systems are illustrated in Fig.5 for Re=1.5.It is observed that the plate free area(F)has a significant impact on the consumption of energy.Emdecreases with an increase in the plate free area.Moreover,the in fluence of F on energy consumption is found to be more profound at smaller values.It is because of the fact that at smaller plate free area,the resistances against the flow significantly increases which results in a remarkable increase in the pressure drop along the column.

Fig.5.In fluence of plate free area F on energy consumption for differentchemicalsystems at Re=1.5 and h=0.83.

3.3.The characteristic velocity concept

The applicability of Gayler and Pratt's model[24]for an L-shaped extraction column depends on the linearity of U0plot.Fig.6 shows the flooding point data based on Eq.(13)for the chemical systems studied in this work.According to Fig.6,the slope of lines is twice the value of characteristic velocity.Moreover,the concept of U0can be de fined for the L-shaped extraction column due to the linear plots,although there is a slight deviation in some experiments.Also,it has been found that the characteristic velocity declines with increasing Af and also U0has higher value in the chemical systems with higher interfacial tension.The resulting characteristic velocity values are given in Table 3.

In this work,Eq.(18)is also correlated to the experimental Udfobtained from the variation of pressure drop through the column length and the exponent n as well as U0are presented in Table 4 for three liquid–liquid systems.Fig.7 shows the flooding point data based on Eq.(18).It was apparent that the characteristic velocity method based on Richardson and Zaki's Eq.(19]is applicable for an L-shaped extraction column due to the linear plots through the origin point for different chemical systems.According to literature,the parameter of Richardson and Zaki model is different in various columns.Godfrey and Slater[20]revealed that n varies between 0 and 4 for rotating disc contactors,0.3 to 1.5 for packed columns.Moreover,this range is noted for perforated-plate columns from-3 to 1[25],for Graesser raining bucket contactors from-0.9 to 3.6[26]for Hanson mixer–settler extraction columns from-6 to 6[27]and for multiimpeller columns from 1 to 9[28].The values found in this research are in satisfactory agreement with Godfrey and Slater's[20]values for perforated-plate columns.

Fig.6.Characteristic velocity plots of flood point data under different pulsation intensities based on Gayler and Pratt's model[24]for(a)toluene–water(b)butyl acetate–water and(c)butanol–water.

Table 3 Characteristic velocities under different pulsation intensities

Table 4 Characteristic velocities under different pulsation intensities

Fig.7.Characteristic velocity plots of flood point data under different pulsation intensities based on Richardson and Zaki model for(a)toluene-water(b)butyl acetate-water and(c)butanol-water.

4.Conclusions

In this research,the feasibility of a novel L-shaped pulsed sieveplate column for solvent extraction applications is investigated.In this regard,an evaluation on the energy consumption of the column is conducted due the variation of two-phase pressure drop which is previously reported[13].The in fluences of pulsation intensity and the geometrical parameters including the plate spacing and plate free area on the energy consumed are determined.A correlation for determination of mean energy consumption in column apparatuses with perforated plates in case of pulsed flow is proposed.It is useful for design purposes,namely for determination of energy losses due to pressure drop at different geometry parameters of the column–plate free area and interpolate distance and at different pulsation parameters.The results are helpful for optimization of column geometry targeted to lower energy consumption.

Furthermore,the concept of the characteristic velocity,which is an important parameter in design of an extractor,is investigated as well.The applicability of characteristic velocity approaches including the Gayler and Pratt's model[24]and Richardson and Zaki model[19]is evaluated and it is apparent that both methods can be used for designing the L-shaped extraction columns;however,the Richardson and Zaki model provides much more accurate results.

Nomenclature

A amplitude of pulsation,m

Af pulsation intensity,m·s-1

a specific interfacial area,m2·m-3

C pressure drop coefficient for a permanents flow(in Eq.(1))

Cppressure drop coefficient for a pulsed flow(in Eq.(9))

CpEpressure drop coefficient in Eq.(18)

Dccolumn diameter,m

Emmean energy per unity of mass and time,pulsed flow,J·s-1·kg-1

E(t) instantaneous energy,pulsed flow,J·s-1·kg-1

Etenergy per unity of mass and time,permanent flow,J·s-1·kg-1

F plate free area

FNforce exerted Perpendicular to the cross section,N·m-2

f frequency of pulsation,Hz

g gravity,m·s-2

H interplate distance,m

h geometry ratio,=H/Dc

Δl differential manometer height,m

Δp pressure drop,Pa

Re Reynolds number

S column cross section,m2

t time,s

U velocity,m·s-1

Ucsuper ficial velocity of continuous phase,m·s-1

Udsuper ficial velocity of dispersed phase,m·s-1

Ummean velocity,pulsed flow,m·s-1

Uslipslip velocity,m·s-1

U(t) instantaneous flow velocity,pulsed flow,m·s-1

U0characteristic velocity,m·s-1

X distance between measuring points,m

μ viscosity,N·s·m-2

ρ density,kg·m-3

σ interfacial tension between two phases,N·m-1

? kinematic viscosity,m2·s-1

φ holdup

Subscripts

c continuous phase

d dispersed phase

f flooding

m mixture

Acknowledgments

The authors thank the reviewers for constructive and helpful comments that led to de finite improvement in the paper.The authors also thank SchoolofChemicalEngineering,College ofEngineering,University of Tehran,for the financial support.

References

[1]M.Asadollahzadeh,A.Ghaemi,M.Torab-Mostaedi,S.Shahhosseini,Experimental mass transfer coefficients in a pilot plant multistage column extractor,Chin.J.Chem.Eng.24(2016)989–999.

[2]Y.Wang,K.H.Smith,K.Mumford,T.F.Grabin,Z.Li,G.W.Stevens,Prediction of dispersed phase holdup in pulsed disc and doughnut solvent extraction columns under different mass transfer conditions,Chin.J.Chem.Eng.24(2016)226–231.

[3]R.L.Yadav,A.W.Patwardhan,Design aspects of pulsed sieve plate columns,Chem.Eng.J.138(2008)389–415.

[4]P.Amani,M.Amani,M.Mehrali,K.Vajravelu,In fluence of quadrupole magnetic field on mass transfer in an extraction column in the presence of MnFe2O4nanoparticles,J.Mol.Liq.238(2017)145–154.

[5]P.Amani,M.Amani,R.Hasanvandian,Investigation of hydrodynamic and mass transfer of mercaptan extraction in pulsed and non-pulsed packed columns,Korean J.Chem.Eng.34(2017)1456–1465.

[6]P.Amani,J.Safdari,A.Gharib,H.Badakhshan,M.H.Mallah,Mass transfer studies in a horizontal pulsed sieve-plate column for uranium extraction by tri-n-octylamine using axial dispersion model,Prog.Nucl.Energy 98(2017)71–84.

[7]F.Panahinia,J.Safdari,M.Ghannadi-Maragheh,P.Amani,M.H.Mallah,Modeling and simulation ofa horizontalpulsed sieve-plate extraction column using axialdispersion model,Sep.Sci.Technol.52(9)(2017)1537–1552.

[8]F.Panahinia,M.Ghannadi-Maragheh,J.Safdari,P.Amani,M.-H.Mallah,Experimental investigation concerning the effect of mass transfer direction on mean drop size and holdup in a horizontalpulsed plate extraction column,RSC Adv.7(2017)8908–8921.

[9]P.Amani,M.Amani,R.Saidur,W.-M.Yan,Hydrodynamic performance of a pulsed extraction column containing ZnO nanoparticles:Drop size and size distribution,Chem.Eng.Res.Des.121(2017)275–286.

[10]P.Amani,M.Esmaieli,Drop behavior characteristics in different operating regimes in an L-shaped pulsed sieve-plate column,Can.J.Chem.Eng.(2017)https://doi.org/10.1002/cjce.22911,http://onlinelibrary.wiley.com/adranced/search/results.

[11]C.Hanson,Recent Advances in Liquid–Liquid Extraction,Elsevier,1971.

[12]S.Akhgar,J.Safdari,J.Tow fighi,P.Amani,M.H.Mallah,Experimental investigation on regime transition and characteristic velocity in a horizontal–vertical pulsed sieve-plate column,RSC Adv.7(2017)2288–2300.

[13]P.Amani,J.Safdari,H.Abolghasemi,M.H.Mallah,A.Davari,Two-phase pressure drop and flooding characteristics in a horizontal–vertical pulsed sieve-plate column,Int.J.Heat Fluid Flow 65(2017)266–276.

[14]T.Mí?ek,R.Berger,J.Schr?ter,Standard test systems for liquid extraction studies,EFCE Publ.Ser.46(1985)1.

[15]J.D.Thornton,Liquid-liquid extraction.Part XIII:The effect of pulse wave-form and plate geometry on the performance and throughput of a pulsed column,Trans.Inst.Chem.Eng.36(1957)316–330.

[16]M.S.Aoun,Numerical simulation of hydrodynamics and axial mixing in pulsed extraction columns with discs and doughnuts,PhD Thesis.INP-Toulouse,France,1995.

[17]J.F.Milot,J.Duhamet,C.Gourdon,G.Casamatta,Simulation of a pneumatically pulsed liquid–liquid extraction column,Chem.Eng.J.45(1990)111–122.

[18]J.Thornton,H.Pratt,Liquid–liquid extraction:Part VII, flooding rates and mass transfer data rotary annular columns,Trans.Inst.Chem.Eng.31(1953)4.

[19]J.Richardson,W.Zaki,Fluidization and sedimentation—Part I,Trans.Inst.Chem.Eng.32(1954)38–58.

[20]J.Godfrey,M.Slater,Slip velocity relationships for liquid–liquid extraction columns,Chem.Eng.Res.Des.69(1991)130–141.

[21]F.R.Dell,H.R.C.Pratt,A note on the correlation of flooding rates for packed gasliquid columns,J.Appl.Chem.2(2007)429–435.

[22]T.Miyauchi,H.Oya,Longitudinal dispersion in pulsed perforated-plate columns,AIChE J.11(1965)395–402.

[23]M.M.Hafez,J.Procházka,The dynamic effects in vibrating-plate and pulsed extractors-I.Theory and experimental technique,Chem.Eng.Sci.29(1974)1745–1753.

[24]R.Gayler,H.Pratt,Holdup and pressure drop in packed columns,Trans.Inst.Chem.Eng.29(1951)110–125.

[25]A.Hamidi,M.Van Berlo,K.C.A.M.Luyben,L.A.M.Van Der Wielen,Flooding characteristics of aqueous two-phase systems in a countercurrent sieve-plate column,J.Chem.Technol.Biotechnol.74(1999)244–249.

[26]A.D.Giraldo-Zuniga,J.S.R.Coimbra,L.A.Minim,E.E.G.Rojas,Dispersed phase holdup in a Graesser raining bucket contactor using aqueous two-phase systems,J.Food Eng.72(2006)302–309.

[27]M.Napeida,A.H.Asl,Chemical engineering research and design holdup and characteristic velocity in a Hanson mixer–settler extraction column,Chem.Eng.Res.Des.8(2010)703–711.

[28]M.Asadollahzadeh,M.Torab-Mostaedi,S.Shahhosseini,A.Ghaemi,Holdup,characteristic velocity and slip velocity between two phases in a multi-impeller column for high/medium/low interfacial tension systems,Chem.Eng.Process.Process Intensif.100(2016)65–78.