Modeling and Simulation of a Rotating-Disk Contactor for the

Article pubs.acs.org/IECR

Modeling and Simulation of a Rotating-Disk Contactor for the Extraction of Aromatic Hydrocarbons from a Lube-Oil Cut Amirhossein Mehrkesh,† Touraj Tavakoli,‡ Mohammad Sadegh Hatamipour,‡ and Arunprakash T. Karunanithi*,† †

Department of Civil Engineering, University of Colorado Denver, 1200 Larimer Street, Denver, Colorado 80217, United States Department of Chemical Engineering, University of Isfahan, Hezar-Jerib Avenue, Isfahan, Iran

‡

ABSTRACT: Previously, several mathematical models have been proposed for liquid−liquid extraction processes involving a rotating-disk-contactor (RDC) column. Most of these models reveal that hydrodynamic and mass-transfer phenomena are important for predicting the performance of the column. In this paper, a mathematical model, using a new scheme, was developed to acquire a simulation tool to predict the performance of a RDC column used in lubricating-oil production. Field data obtained in a RDC column of 4.1 m diameter, 22.2 m height, and 32 disks, from a commercial lubricating-oil production company, were used to evaluate the predictions. The model is used for parametric study to investigate the effects of operational data such as the solvent and feed temperatures, solvent-to-feed ratio, and disk rotation rate on the extraction yield.

1. INTRODUCTION It is necessary to remove aromatic hydrocarbons from lube-oil cuts to improve the overall quality of produced lubricating oils.1,2 Separation of aromatic components from a lube-oil cut is usually carried out by liquid−liquid extraction. Furfural is the commonly used solvent in this process because its selectivity toward aromatic compounds is high.3−5 The production of lubricating oils in a liquid−liquid extraction process is accomplished by contacting the feed and solvent in an agitating extraction column. A widely used type of extractor in industry is the rotating-disk contactor (RDC), which is a mechanically agitated extraction column. A comparison between several conventional contactor devices shows that RDCs are the most efficient extraction systems in terms of extraction yield.6 Other RDC advantages include very high throughput, low power consumption, ease of operation, and maintenance.6 In a RDC, a central shaft positioned in the axis of the column carries a number of equally spaced rotor disks, placed in the middle of the compartments formed by the stator rings. A variable-speed gear motor drives the shaft. The agitation provided by the disks mounted on the rotor shaft improves the performance of the RDC by breaking the dispersed-phase droplets and increasing the interfacial area of mass transfer.7 Extraction is attained by introducing the light liquid phase at the bottom of the column and the heavy phase at the top of the column.7 Several studies have attempted to define the efficiency of a RDC based on the physical properties and geometry of the system.8 However, because of the complexity of the extraction process, modeling of a RDC column to a high degree of accuracy has proven to be difficult. In the past few years, several studies have focused on the simulation of hydrodynamics in countercurrent stirred liquid−liquid extraction columns.9 Modes and Bart10 investigated the velocity profile of single-phase water flow with the help of the computational fluid dynamics (CFD) code FIDAP. Kolb11 simulated the single-phase flow in a Kühni column and compared it with particle image velocimetry (PIV) experiments. Velocity fields in a single-phase-flow RDC were measured using © 2013 American Chemical Society

laser doppler velocimetry and simulated with CFD by Fei et al.12 Rieger et al.13 investigated the one- and two-phase flow in a RDC extraction column employing Euler−Euler and Euler− Lagrange models but experienced problems with convergence. Haderer14 investigated different turbulence models for the onephase flow and applied the Euler−Euler model for two-phaseflow simulations. Most of these studies focused on the computational simulation of flow patterns (concentration, velocity, and temperature profile) in a RDC column to study the effects of those patterns on the performance of the column. Although these approaches seem to be more accurate and more comprehensive than flow models such as backflow or dispersion, they were not considered in this study because an actual industrial RDC column was used and validation of the CFD model using PIV or other related approach was not feasible. In addition, modeling of a RDC column using datadriven models such as artificial neural networks has been used.15,16 Application of data-driven models requires a broad range of operational field data (hundreds of data sets), which is not usually accessible. Therefore, in this work, we focus on the development of a comprehensive simulation model of an industrial RDC column with the aim to find the optimal operational conditions (the best performance) without any changes in the scale or geometry of an existing column. Toward this end, we developed a new approach that considers a more detailed spatial representation of a RDC column as a series of fully mixed compartments. The proposed model will be useful to optimize different operational parameters, such as solvent and feed temperatures, solvent-to-feed ratio, and disk rotation rate. It could also be used to minimize the consumption of furfural (an environmental pollutant) by identifying the optimal solvent-to-feed ratio. The model can also be utilized to Received: Revised: Accepted: Published: 9422

December 12, 2012 April 7, 2013 May 13, 2013 May 13, 2013 dx.doi.org/10.1021/ie303427m | Ind. Eng. Chem. Res. 2013, 52, 9422−9432

Industrial & Engineering Chemistry Research

Article

Figure 1. General scheme of the RDC column as a series of compartments.

There is a rotating disk installed on the column axial shaft in the middle of each compartment that causes breakage of larger liquid drops into smaller ones, thereby increasing the masstransfer area between the two phases. The mass-transfer rate in a RDC column is affected by the holdup of liquid droplets in the mixing compartments, concentration gradient, and diameter of the liquid droplets. It is worth noting that there is no interstage settling in RDCs. During the extraction process, within each compartment, the feed is separated into raffinate and extract phases. The raffinate is the light phase which moves toward the top of the RDC in the form of liquid drops because of the buoyancy force, and plays the role of feed to the next compartment. The extract phase is the heavy phase and moves toward the bottom of the RDC because of gravitational force. The output extract phase of each compartment plays the role of solvent to its bottom compartment. This process continues from the bottom of the column to the top. Finally, in the settling zone, the raffinate phase, which is the main product, exits from the top of the RDC column and the extract phase exits from the bottom of the column. For modeling of the RDC column, we considered an integrated approach, which is more relevant than a differential approach because of the difficulty in defining the boundary conditions and accounting for the lumped nature of the parameters that characterizes lubricating

determine the desirable temperature slope in the column, which could help prevent undesirable energy losses. Additionally, we could study the effect of physical properties of the solvent on the extraction yield. Further, identification of more environmentally benign solvents, such as ionic liquids, as replacements for furfural would require a predictive and simulation model for RDC. This capability is not available in current commercial process simulators. The proposed model can handle any new solvent as long as the relevant physicochemical properties are available. This will greatly facilitate the integration of other methods such as computer-aided molecular design17 and computer-aided ionic-liquid design18 with RDC simulation to design and predict the extractor performance using new solvents.

2. MATHEMATICAL MODEL DEVELOPMENT In a typical lubricating-base-oil production process, a RDC extractor is used, to remove aromatic fractions from a lube-oil cut, through liquid−liquid extraction. As discussed before, furfural is conventionally used as an extraction solvent in this process. The lube-oil cut from the vacuum crude-oil distillation column is fed to the RDC from the bottom of the column. This is converted to liquid droplets by passing through nozzles. The extraction solvent, furfural, is fed to the RDC from the top. 9423

dx.doi.org/10.1021/ie303427m | Ind. Eng. Chem. Res. 2013, 52, 9422−9432


Article

and solvent in the raffinate phase entering the nth stage. Ca,n, Cs,n, and Cf,n are the respective steady-state concentrations of aromatics, saturated, and solvent in the raffinate phase exiting from the nth stage. C*a,n, C*s,n, and C*f,n are the equilibrium concentrations. Kaod, Ksod, and Kfoc are the overall mass-transfer coefficients of aromatics, saturated, and furfural, respectively. a and V are the mass-transfer area and compartment volume, respectively. Axial mixing in dispersed and continuous phases may lead to a back-mixing phenomenon. As a result, a fraction of each phase flows opposite to their normal flow direction from one compartment to the other. Typically, the mass flow due to this phenomenon in the dispersed phase is negligible in comparison to the continuous phase. The back-mixing parameter, e, can be defined as follows:

oils. The key difference between the proposed model and other existing RDC models is the explicit representation of the RDC column as a set of individual compartments. The more detailed formulation of the proposed model improves the accuracy of the prediction for the following reasons: (1) accounting for the temperature variation across the column instead of considering a constant temperature for each phase; (2) explicit consideration of all possible multicomponent mass transfers between the two phases instead of only considering mass transfer of the solute from the feed to solvent; (3) accounting for variation in the physical properties, flow rates, and mass-transfer coefficients as a function of the temperature and composition across the column. In the proposed model, the temperatures and concentrations of all components are assumed to be constant in each compartment but vary across different compartments. This is possible because an axial-mixing approach is applied within each compartment. This section provides a detailed description of the developed RDC model. The extraction column was considered as a series of continuously stirred compartments (i.e., uniform axial-mixing assumption), as shown in Figure 1. The compositions of the raffinate and extract streams exiting each compartment are equal to their compositions inside them. The generic mass-balance equations for the three components (aromatics, saturated compounds, and solvent) in two phases (raffinate and extract) for the nth stage are given by eqs 1−6.

e=

2/3 2 ⎛ 0.00679 ⎞1/3⎛ NDR ⎞⎛ DR ⎞ ⎛ DS ⎞ ⎜ ⎟ e= ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ H ⎠ ⎝ Vc ⎠⎝ DC ⎠ ⎝ DC ⎠

(1)

[Q c, n + 1(1 + e)Cs,̅ n + 1 + Q c, n − 1eCs,̅ n − 1] − [Q c, n(1 + e)Cs,̅ n − Q c, neCs,̅ n] (2)

a=

[Q c, n + 1(1 + e)Cf,̅ n + 1 + Q c, n − 1eCf,̅ n − 1] f = Koc aV (Cf,̅ n − C̅ *f, n )

(9)

0.26 ⎛ V ⎞ ⎛ μc φ = C1 exp(0.59FrR )⎜1 + c ⎟ ⎜⎜ Vd ⎠ ⎝ γDR ρc ⎝

(3)

a Q d, n − 1Ca, n − 1 − Q d, nCa, n = Kod aV (Ca, n − Ca,*n)

Q d, n − 1Cs, n − 1 − Q d, nCs, n =

6φ d32

where φ is the dispersed-phase holdup, which can be estimated as follows:22

− [Q c, n(1 + e)Cf,̅ n − Q c, neCf,̅ n]

s Kod aV (Cs, n

(8)

where H is the compartment height, DR is the rotor diameter, DC is the column diameter, DS is the stator diameter, N is the rotation rate, and Vc is the velocity of the continuous phase. The following assumptions were made: the radial concentration distribution is ignored, the back-mixing phenomenon in the dispersed phase is negligible, the droplets are spherical in shape with a constant diameter, the temperature equilibrium exists between the two phases in each compartment, and the heat of mixing is negligible (derived from the experimental results). The mass-transfer area, a, required in the mass-balance equations is calculated using the following equation:21

− [Q c, n(1 + e)Ca,̅ n − Q c, neCa,̅ n]

s = Kod aV (C*s, n − Cs, n)

(7)

The back-mixing parameter can be estimated based on the column’s geometrical properties, rotation rate, and velocity of the continuous phase using eq 8.20

[Q c, n + 1(1 + e)Ca,̅ n + 1 + Q c, n − 1eCa,̅ n − 1] a = Kod aV (C*a, n − Ca, n)

fraction of streams that are mixed indirectly fraction of streams that flow directly

− Cs,*n)

f Q d, n − 1Cf, n − 1 − Q d, nCf, n = Koc aV (C̅ *f, n − Cf,̅ n)

(4)

⎛ Δρ ⎞−0.56⎛ DR 2ρ g ⎞0.15⎛ H ⎞−1.18 c ⎟ ⎜⎜ ⎜⎜ ⎟⎟ ⎟ ⎜ ⎟ ⎝ ρc ⎠ ⎝ γ ⎠ ⎝ DR ⎠

(5)

⎞0.12 ⎛ V 2 ⎞0.42 ⎟ ⎜ d ⎟ ⎟ ⎠ ⎝ DR g ⎠

(10)

where Vc and Vd are the respective velocities of the continuous and dispersed phases, which can be calculated using the following equations:

(6)

where Qc,n+1, Qc,n, and Qc,n−1 are the respective flow rates of the extract (continuous) phase entering into, exiting from, and backflowing into the nth stage. C̅ a,n+1, C̅ s,n+1, and C̅ f,n+1 are the respective steady-state concentrations of aromatics, saturated, and solvent in the extract phase entering the nth stage. C̅ a,n, C̅ s,n, and C̅ f,n are the respective steady-state concentrations of aromatics, saturated, and solvent in the extract phase exiting the nth stage. C̅ a,n−1, C̅ s,n−1, and C̅ f,n−1 are the respective steady-state concentrations of aromatics, saturated, and solvent in the backflow extract phase entering the nth stage. Qd,n−1 and Qd,n are the respective flow rates of the raffinate phase entering into and exiting from the nth stage. Ca,n−1, Cs,n−1, and Cf,n−1 are the respective steady-state concentrations of aromatics, saturated,

Vc =

Vd =

Qc

1 A C 3600

Qd Qc

Vc

(11)

(12)

where AC is the cross-sectional area of the RDC column and Qd and Qc are the flow rates of the dispersed and continuous phases, respectively. The value of C1 is fixed at 1.37, 1.43, and 1.26 for the cases of without mass transfer, with mass transfer from the continuous phase to the dispersed phase, and with 9424



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mass transfer from the dispersed phase to the continuous phase, respectively. The overall mass-transfer coefficients for component i, Kiod and Kioc, are estimated as follows: mi 1 1 + i i = Kod kci kd

Dij̅ = (D̅ °ij )(1 + xj − xi)/2 (D̅ ° ji )(1 + xi − xj)/2

Using the created matrix of Maxwell−Stephan diffusion coefficients of the components in the concentrated system, the matrix of B is created as follows:

(13)

1 1 1 i = i + Koc kc mikdi

x Bii = i + Din̅

(14)

kdi

=

(15)

Shdi Di ,eff

mi =

d32

(16)

Di ,eff = Dii

The characteristic length of the column (d32) is estimated as follows:23 ⎞⎛ μ c ⎟⎟⎜⎜ ⎠⎝ γρc DR

(18)

Shdi

(19)

Shc,i ∞

1/3 1.7

)

(27)

−

Shci

= C2Re

n ⎛ Vslipμc ⎞ Scci 2⎜ ⎟

n1

n1

1 ⎝ γ ⎠ 1 + k n4

(28)

where Re represents the Reynolds number, Scid represents the Schmidt number of component i in the dispersed phase, and ρd and ρc are the respective densities of the dispersed and continuous phases. κ is the ratio of viscosities of the continuous (μc) and dispersed (μd) phases, g is the acceleration due to gravity, and γ is interfacial tension. Scic represents the Schmidt number of component i in the continuous phase, V slip represents the slip velocity, and Shic,∞ is the maximum possible Sherwood number for component i, which is estimated as a function of the Peclet number using eq 36. Shic,rigid is the minimum possible Sherwood number for rigid droplets for component i estimated as a function of the Schmidt and Reynolds numbers using the correlation shown in eq 32. The following values are assumed for the other constants:

9.89 × 10−8Vj̅ 0.265T μj 0.907 Vi̅ 0.45

(26)

⎛ ρ ⎞2/3 ⎜ d⎟ = 17.7 + 1/3 ⎜ ⎟ 1 + 1.43 × 10−2(ReScdi ) ⎝ ρc ⎠ ⎡ ⎧ ⎛ ρ ⎞1/4 ⎪ ⎫n 2 ⎤ φ c 1 ⎢1 + C ⎪ ⎨ ⎜ ⎟ ⎬ ⎥ 2⎪ 2/3 ⎢ ⎪ ⎥ 1+κ ⎣ ⎩ g ⎝ gγ ⎠ ⎭ ⎦ 3.19 × 10−3(ReScdi

i Shci − Shc,rigid

γ is the interfacial tension, which is related to the surface tension of the two phases, and its estimation is fully explained in the correlative physical properties section. To calculate the effective diffusion coefficients of the components in two phases, the following approach is applied. The Maxwell−Stephan diffusion coefficients for system components in an infinitive-dilution situation are calculated based on the Siddiqui and Lucas correlation, which has very high accuracy for hydrocarbon mixtures.24 D̅ °ij =

i = 3 (furfural)

(25)

Previous research22 shows that, for RDC columns, n2 = 0.33 and C2 = 0.

DR 2Nρc μc

(24)

The Sherwood numbers for component i in the continuous (Shic) and dispersed phases (Shid) are calculated by the approach detailed in the following:19

The value of C1 is fixed at 0.63, 0.74, and 0.53 for the cases of without mass transfer, with mass transfer from the continuous phase to the dispersed phase, and with mass transfer from the dispersed phase to the continuous phase, respectively. FrR is the Froude number of the column, which is calculated as follows: FrR =

(23)

i = 1, 2 (aromatics and saturated)

Di ,eff = Bii−1

⎞−0.12 ⎛ ρ ⎞0.16 ⎟ ⎜⎜ d ⎟⎟ ⎟ ⎝ ρc ⎠ ⎠

⎛ D 2ρ g ⎞−0.59⎛ H ⎞0.25⎛ D ⎞0.46 ⎜⎜ R c ⎟⎟ ⎜ ⎟ ⎜ C⎟ ⎝ DC ⎠ ⎝ DR ⎠ ⎝ γ ⎠

(22)

Finally, effective diffusion coefficients of the components in the two phases are estimated as follows:

(17)

⎛ d32 C1 = ⎜⎜ DR ⎝ 0.07 + FrR

k=1 i≠k

xk Dik̅

[D] = [B]−1 [Γ]

Cdi * Cci *

∑

where n is the total number of components in the system. Bii elements are located on the main diagonal of the matrix. In the next step, the matrix Γ, representing the activity coefficients of the components, is calculated using the NRTL approach by considering the temperature of the compartment.25 The Fickian diffusion coefficients on the volumetric basis are calculated as follows:

Shci Di ,eff d32

n

⎛1 1 ⎞⎟ Bij = −xi⎜⎜ − Din̅ ⎟⎠ ⎝ Dij̅

where kci and kdi represent the individual mass-transfer coefficients of component i in the continuous and dispersed phases, respectively, and mi is the equilibrium distribution coefficient of component i. kic and kid are expressed as a function of the Sherwood number (Sh), effective diffusivity (Di,eff), and characteristic length (d32) as follows:

kci =

(21)

(20)

Maxwell−Stephan’s diffusion coefficients for the components in a concentrated mixture are calculated based on the mole fraction and infinitive-dilution diffusion coefficients as follows: 9425



Re =

Vslip =

Article

d32Vslipρc μc

Dynamic Viscosity. The correlations developed to estimate the dynamic viscosities of the aromatics and saturated components are shown in eqs38 and 39. The dynamic viscosity correlation for furfural (eq 40) was taken from the literature.

(29)

Vd Vc + φ 1−φ

⎡ μaromatics = exp⎢ −931.6505 + 131.987 ln(T ) ⎣

(30)

26

Shic, ∞ = C1 +

+

2 (Pei)1/2 π

(31)

n

n3

(32)

(39)

19

⎡ 3950.4 ⎤ μfurfural = exp⎢ −69.008 + 8.655 ln(T ) + ⎣ T ⎥⎦

C1 = 50, C2 = 5.26 × 10−2 , n1 1 1 = + 6.59 × 10−2Re1/4 , n2 = n3 = , n4 = 1.1 3 3

The Schmidt numbers of the system components are calculated using eqs 34 and 35 for the continuous and dispersed phases. μc Scci = ρc Di ,eff (34)

ln(μmix ) =

(35)

σsaturated = −0.067T + 43.121

(36)

(43)

R2 = 0.985

(44)

R2 = 0.97 (45)

The energy balance across the column is written based on the thermal equilibrium assumption in each compartment, and the output temperatures of both phases are considered to be equal to the temperature in the compartment. The energy balance for the nth stage is shown in eq 37.

By the use of pure-component surface tension values and mole fractions and application of the appropriate mixing rule, the surface tension of each phase is calculated by eq 46.

σmix =

Wc, nCpc, n (Tn − Tref ) + Wd, nCpd, n (Tn − Tref )

∑ xiσi

(46)

The interfacial tension for two available phases (continuous and dispersed) in a RDC column is one of the most important parameters in the performance of the column. This term is defined as the difference between the surface tension of two phases and that of air. In the following equation, A and B refer to the two liquid phases and C refers to air. γAB = σAC − σBC (47)

= Wd, n − 1Cpd, n − 1 (Tn − 1 − Tref ) + Wc, n + 1Cpc, n + 1 (Tn + 1 − Tref )

R2 = 0.96

1.1124 ⎛ T ⎞⎟ σfurfural = +0.08429⎜1 − ⎝ 670.1 ⎠

d32Vslip Di ,eff

(41)

σaromatics = −0.0596T + 61.837

The Peclet number is calculated using eq 36. Pei =

∑ xi ln μi

Surface Tension. The following correlations were regressed (as described before) for estimating the surface tension of the three components.

μd ρd Di ,eff

(40)

By the use of pure-component dynamic viscosities and mole fractions and application of the appropriate mixing rule, the dynamic viscosity of each phase is calculated by eq 41.

(33)

Scdi =

(38)

⎡ −6612.4915 ⎤ μsaturated = exp⎢153.8385 − 22.728 ln(T ) + ⎥⎦ ⎣ T

19

Shic,rigid = 2.43 + 0.775Re1/2Scci 3 + 0.0103ReScci

57865.758 ⎤ ⎥⎦ T

(37)

Correlative Equations for the Physical Properties of the Components. In this section, we describe the estimation of various physical properties and equilibrium distribution coefficients within each compartment as a function of the temperature and compositions using mixing rules. The aromatics and saturated compounds in the feed (petroleum lube-oil cut) are a mixture of several hydrocarbons. Therefore, in order to estimate the average physical property values, we characterized multiple industrial raffinate samples, with different compositions, using ASTM-D3238 and ASTM-D2502. The dynamic viscosity and density of the samples were measured with an Anton Paar SVM3000 instrument according to ASTM D-7042. The surface tension values of the samples were estimated using the Sugen equations.27 The heat capacities of the samples were measured using a bomb calorimeter. By the use of these data and application of the appropriate mixing rules, several physical property correlations for aromatic, saturated, and furfural components were developed.28−31

Density. The correlations developed for density are shown in eqs 48−50. The mixing rule used to estimate the density of two phases is shown in eq 51. 1 + 1105 T

R2 = 0.99

1 + 578.16 T

R2 = 1

ρaromatics = 90774 ρsaturated = 76618 ρfurfural = 89832

mixing rule: 9426

1 + 864.78 T

1 = ρmix

∑

R2 = 0.987

(48)

(49)

(50)

yi ρi

(51)



Article

Heat Capacity. The correlations developed for the heat capacity are shown in eqs 52−54. The mixing rule used is shown in eq 55. Cparomatics = 0.0034T + 0.2564

R2 = 0.96

(52)

Cpsaturated = 0.0048T + 0.5344

R2 = 0.98

(53)

Cpfurfural = 0.003116T + 0.7691 Cpmix =

∑ yCp i i

R2 = 0.99

(54) (55)

Equilibrium Distribution Coefficient. The equilibrium concentrations used in this study are based on Montahaie et al.’s work.32 For the three components aromatics, saturated, and furfural, the equilibrium distribution coefficients are developed using an exponential correlation as shown in eq 56.

m = a exp(bR )

Figure 2. Aromatics distribution coefficients versus the solvent-to-feed ratio.

(56)

where R is the solvent-to-feed ratio and a and b are the correlative parameters for each component. A few correlations developed to calculate a and b based on the temperature are listed in the following equations. For aromatics: a = −0.0006T + 0.9789

(57)

b = −0.003T + 1.4615

(58)

For saturated: a = 0.0022T + 2.719

(59)

b = −0.0029T + 1.9943

(60)

Figure 3. Saturated distribution coefficients versus the solvent-to-feed ratio.

For furfural: a = 0.0009T − 0.088

(61)

b = 0.0012T − 0.7163

(62)

Equations 38−62 are valid within the temperature range of 80− 130 °C, which is the applicable range for the performance of this RDC column. This limitation for the temperature range is determined by the consideration of two different boundaries: (1) the lowest temperature in which the feed can be entered to column and (2) the maximum allowable temperature for the solvent, which is below the boiling point of furfural. The distribution coefficients (m) related to the three components (saturated, aromatics, and furfural) are shown in the following figures (Figures2−4). By the use of these coefficients for each component and having the respective concentration in one phase, the equilibrium concentration of that component in the other phase can be calculated using eq 17.32 The mathematical modeling flowchart is shown in Figure 5. The convergence criterion was based on the differences between the temperatures, flow rates, and compositions in steps 3 and 7, being less than 0.1% of their respective values. The developed RDC model is generic in nature, can be used for any system, and is not limited to the solvent extraction of aromatic compounds from a lube-oil cut. All mass and energy balance equations, mass-transfer correlations, and hydrodynamic correlations (eqs 1−37) can be utilized for modeling any liquid−liquid extraction process by RDC. However, eqs 38−62 are new correlations created specifically for this case

Figure 4. Furfural distribution coefficients versus the solvent-to-feed ratio.

study. These correlations are related to the physical properties of the three main components in the feed (lube-oil cut).

3. RESULTS AND DISCUSSION 3.1. Model Validation. The motivation to develop a new model for a rotating-disk liquid−liquid extraction contactor for the lubricating-oil extraction process is to acquire the ability to more accurately perform parametric studies of the column with an aim toward investigating the effect of operational parameters such as the feed and solvent temperatures, solvent-to-feed ratio, and rotating rate on the product yield. Before a parametric study can be performed, the model and its accuracy to predict the performance of the extraction process needs to be validated. In order to validate the model accuracy and evaluate the model 9427



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column) were obtained. Operational parameters such as the feed and solvent temperatures, feed and solvent flow rates, and disk rotation rates were incorporated into the model in the form of a databank. Other data including the RDC top and bottom temperatures, lubricating-base-oil flow rates, and compositions of the final raffinate and extract phases were calculated. Comparisons between the actual data and model predicted values are shown in Figure 6a−c.

Figure 5. Mathetatical modeling flowchart.

predictions, we compare the actual data from an operational column with the predicted data from the developed model. The actual data were obtained from a large lubricating-oil production plant. The specifications of this commercial RDC column are listed in Table 1. Table 1. Characteristics of a RDC Column Specification column diameter (m) no. of disks column height (m) feed entry solvent entry

4.1 32 22.2 32nd disk (bottom) 1st disk (top)

In this plant, a lube-oil cut enters the RDC column as the feed and furfural enters the RDC as the solvent. The experimentally measured properties of the lube-oil cut and furfural used in this study are listed in Table 2. For the purpose of validating the model, several sets of actual data and model calculated values such as the RDC top and bottom temperatures and lubricating-base-oil flow rate (main product that exits as the raffinate phase from the top of the Table 2. Typical Physical Properties of the Lube-Oil Cut and Furfural physical property

furfural

lube-oil cut

density, at 20 °C (g/cm3) viscosity, at 25 °C (cP) flash point (°C) MW refractive index (RI), at 20 °C CA (%) CN (%) CP (%)

1.1598 1.49 61.7 96 1.5261

0.9255 445 258.3 490 1.52027 24.3 9.8 65.9

Figure 6. Predicted versus the (a) actual RDC top temperature, (b) actual RDC bottom temperature, and (c) actual RDC top product flow rate. 9428



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Table 3. Actual Data versus Predicted Values for the RDC Top and Bottom Temperatures output parameters input parameters

RDC top temperature (°C)

RDC bottom temperature (°C)

solvent temp (°C)

feed temp (°C)

solvent flow rate (m3/h)

feed flow rate (m3/h)

mass fraction of aromatics in feed

actual

model predicted

error (%)

actual

model predicted

error (%)

118.0 116.0 115.0 105.0 110.0 111.0 98.0 95.0 120.0 109.0

81.0 82.2 82.3 76.0 78.0 69.1 83.7 93.8 83.4 78.2

118.9 118.9 121.6 131.1 122.4 115.3 103.3 103.3 122.9 122.9

88.1 88.1 90.1 87.4 87.4 85.4 71.1 71.1 75.8 75.8

24.3 25.1 24.1 24.5 23.7 23.5 24.8 25.0 23.9 24.3

112.0 109.0 110.7 102.0 103.5 103.5 91.2 83.0 106.5 105.0

117.2 105.2 114.3 104.4 109.3 110.1 97.7 94.9 119.3 108.4

4.6 3.4 3.2 2.4 5.6 6.4 7.1 14.4 12.0 3.2

80.2 78.0 81.3 72.0 72.6 75.3 73.8 68.0 76.6 75.7

82.4 83.5 83.5 77.1 79.2 70.7 84.3 73.8 84.8 79.4

2.7 7.0 2.7 7.1 9.1 6.1 14.2 8.5 10.7 4.9

Table 4. Actual Data versus Predicted Values for RDC Output Flow Rates output parameters flow rate of RDC top stream

input parameters

flow rate of the lubricating base oil

solvent temp (°C)

feed temp (°C)



mass fraction of aromatics in feed

actual

model predicted

error (%)

actual

model predicted

error (%)

118.0 116.0 115.0 105.0 110.0 111.0 98.0 95.0 120.0 109.0

81.0 82.2 82.3 76.0 78.0 69.1 83.7 93.8 83.4 78.2

118.9 118.9 121.6 131.1 122.4 115.3 103.3 103.3 122.9 122.9

88.1 88.1 90.1 87.4 87.4 85.4 71.1 71.1 75.8 75.8

24.3 25.1 24.1 24.5 23.7 23.5 24.8 25.0 23.9 24.3

71.5 71.8 72.1 69.3 70.1 67.3 62.7 70.0 73.8 70.4

77.9 77.2 79.1 76.1 76.2 74.6 60.4 59.7 67.7 66.8

8.9 7.5 9.7 9.8 8.7 10.8 3.7 14.7 8.3 5.1

60.3 61.2 59.8 59.5 58.3 60.2 60.0 60.5 61.1 60.3

67.4 66.9 68.6 68.7 67.6 67.0 54.5 53.1 58.7 59.9

11.8 9.3 14.7 14.7 16.0 11.3 9.3 12.2 3.9 0.7

Comparisons show that for most of the selected data the accuracy of the prediction is more than 95%. To have a better understanding, we present the actual output data and compare them with model predictions for a set of operational conditions (Tables 3−5). A comparison between the actual data and the relevant model predicted values is done.

After validation of the model, it can now be used to perform parametric studies of the extraction process. 3.2. Parametric Study. 3.2.1. Effect of the Mixing Rate on the Mass Fraction of Aromatics in the RDC Compartments. The main target of the extraction process in production of lubricating oil, is to separate heavy aromatic hydrocarbons from the lube-oil cut. Considering this fact, the extraction yield can be defined as the amount of aromatic hydrocarbons separated from the feed. The concentration profile of aromatics in dispersed phase (lubricating oils enriched phase) throughout the column in different disk rotation rates are shown in Figure 7. As it can be observed, with an increase in disk rotation rate, the aromatic content in dispersed phase will be decreased in all compartments. To do this parametric study, all the operational parameters except disk rotation rate, were fixed at their average values (based on the range used for each parameter). The other operational parameters were fixed at these values: Tsolvent = 130 °C, Tfeed = 90 °C, and R (solvent-to-feed ratio) = 1.5. 3.2.2. Effect of the Solvent-to-Feed Ratio. A key parameter in the performance of a liquid extraction column is the solventto-feed ratio. Typically, the extraction yield in a liquid−liquid extraction process increases with an increase in the solvent flow rate. However, increasing the solvent flow rate can lead to the column being filled with solvent, thereby reducing the flow rate of the feed and consequently decreasing the flow rate of the main product. The aromatics concentration profiles in the dispersed phase throughout the column at different solvent-to-

Table 5. Actual Data versus Predicted Values for Aromatics Mass Fraction in the Final Product output parameters aromatics mass fraction in RDC top stream

input parameters solvent temp (°C)

feed temp (°C)



actual value

model predicted value

error (%)

118.0 116.0 115.0 105.0 110.0 111.0 98.0 95.0 120.0 109.0

81.0 82.2 82.3 76.0 78.0 69.1 83.7 93.8 83.4 78.2

118.9 118.9 121.6 131.1 122.4 115.3 103.3 103.3 122.9 122.9

88.1 88.1 90.1 87.4 87.4 85.4 71.1 71.1 75.8 75.8

11.5 11.7 12.0 13.3 12.8 14.1 13.4 12.6 11.5 13.0

12.8 13.0 13.1 14.4 14.3 15.2 14.3 13.4 12 14.1

11.3 11.1 9.2 8.3 11.7 7.8 6.7 6.35 4.3 8.5 9429



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rate will increase the extraction yield. In this study, the other operational parameters were fixed at these values: Tsolvent = 130 °C, Tfeed = 90 °C, and R (solvent-to-feed ratio) = 1.5. The results for the above-mentioned operational parameters are shown as a solid line in Figure 9. To do a sensitivity analysis on the results, the fixed parameters are changed by ±10%. The effects of the disk rotation rate on the extraction yield are shown in Figure 9 for both cases, where the fixed parameters were changed by 10%. It can be inferred from the figure that when the disk rotation rate (N) is increased, the same ascending trend for the extraction yield can be observed. 3.2.4. Effect of the Solvent-to-Feed Ratio on the Aromatics Extraction Yield. The extraction yield for different solvent-tofeed ratios is shown in Figure 10. The results show that Figure 7. Profile of the aromatics mass fraction in the dispersed phase at different disk rotation rates.

feed ratios are shown in Figure 8. As can be observed, increasing the solvent-to-feed ratio will decrease the aromatic

Figure 10. Extraction yield versus solvent-to-feed ratios.

increasing the solvent-to-feed ratio will increase the extraction yield. In this study, the other operational parameters were fixed at these values: Tsolvent = 130 °C, Tfeed = 90 °C, and N (disk rotation rate) 2 rpm. To do a sensitivity analysis, these fixed parameters were changed by ±10%. The effect of the solventto-feed ratio on the extraction yield is shown in Figure 10 for the two cases, where the fixed parameters were changed by 10%. As can be observed by the increase of R (solvent-to-feed ratio), the same ascending trend for the extraction yield is observed. 3.2.5. Effect of the Solvent Temperature. The extraction yields for different solvent temperatures are shown in Figure 11. The results indicate that when the solvent and feed temperatures are increased, the extraction yield is increased. The study reveals that the effect of the feed temperature is more important than the temperature gradient within the column with respect to the extraction yield. To clarify this

Figure 8. Profile of the aromatics mass fraction in the dispersed phase at different solvent-to-feed ratios.

content of the dispersed phase in all compartments. In this study, the other operational parameters were fixed at these values: Tsolvent = 130 °C, Tfeed = 90 °C, and N (disk rotation rate) = 2 rpm. 3.2.3. Effect of the Disk Rotation Rate. The extraction yield is defined as the flow rate of aromatics separated from the lubeoil cut divided by the flow rate of aromatics entering the column. The extraction yield for various disk rotation rates is shown in Figure 9. It is apparent that increasing the rotation

Figure 9. Extraction yield versus disk rotation rates.

Figure 11. Extraction yield for different solvent temperatures. 9430



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height on the extraction yield is shown in Figure 13. As can be seen, increasing the compartment height will increase the

statement, further we can say that for the same temperature gradients (Tsolvent − Tfeed) within the column (at different temperatures) we can have different extraction yields. This fact is illustrated below: In Figure 8, the value of the extraction yield is plotted versus the solvent temperature for three different feed temperatures. For example, if Tsolvent = 90 °C and Tfeed = 75 °C, the temperature gradient (ΔT) is equal to ΔT = Tsolvent − Tfeed = 15 °C, and from Figure 8, we can say that the extraction yield is 43%. At the same time, if we have Tsolvent = 105 °C and Tfeed = 90 °C, the temperature difference (ΔT) is again 15 °C, but from Figure 8, we can see that the yield of extraction is 57%. Therefore, with the same temperature differences, we can get different extraction yields based on the selected solvent and feed temperatures. However, increasing the temperature of the feed would result in more energy expenses to heat the lube-oil cut. In this study, the other operational parameters were fixed at these values: N (disk rotation rate) = 2 rpm and R (solvent-tofeed ratio) = 1.5. 3.2.6. Effect of the Rotor Diameter. After studying the effect of the operational parameters on the extraction yield, we investigated the effect of the RDC geometrical properties on the yield. The geometrical properties of a RDC column such as the column diameter, rotor diameter, and compartment height are the most important geometrical features. The extraction yield versus the rotor diameter is shown in Figure 12. We can

extraction yield until a certain point and after that the curve will have a descending trend. In this study, the other operational parameters were fixed at these values: Tsolvent = 130 °C, Tfeed = 90 °C, N (disk rotation rate) = 2 rpm, R (solvent-to-feed ratio) = 1.5. 3.2.8. Effect of the Column Diameter. The extraction yield versus the column diameter is shown in Figure 14. By

Figure 12. Extraction yield versus the rotor diameter.

Figure 14. Extraction yield versus the column diameter.

Figure 13. Extraction yield versus the compartment heights.

see that, with an increase of the rotor diameter, the extraction yield is increased. However, this increase will be restricted by design limitations. Figure 12 is plotted based on the fixed operational parameters chosen for this study. The other operational parameters were fixed at these values: Tsolvent = 130 °C, Tfeed = 90 °C, N (disk rotation rate) = 2 rpm, and R (solvent-to-feed ratio) = 1.5. 3.2.7. Effect of the Compartment Height. By a decrease of the number of rotating disks in a RDC column as the total height of the column remains fixed, the individual compartment heights were increased (the distance between two disks). Increasing the compartment height in a RDC column will increase the volume of the mixing chambers. This increase has two opposite effects on the extraction yield. On the one hand, because of an increase of the mass-transfer area, the masstransfer rate will increase. On the other hand, by an increase of the compartment height, the amount of solvent and feed will increase in each chamber. When the compartment heights are increased and the power of the rotating disks are kept constant, the volume of solvent and feed in each compartment increase, and as a result the breakage of droplets in the raffinate phase due to disk rotation will be lowered. Consequently, the area of mass transfer will be lowered. The effect of the compartment

increasing the column diameter, the area of mass transfer in each compartment will be increased, which will lead to a higher extraction yield. However, this increase will be restricted by design limitations. In this study, the other operational parameters were fixed at these values: Tsolvent = 130 °C, Tfeed = 90 °C, N (disk rotation rate) = 2 rpm, R (solvent-to-feed ratio) = 1.5.

4. CONCLUSION This paper presents a new approach toward simulation of a RDC column used in lubricating-oil production. The developed model compares more favorably with other existing backflow models by consideration of the temperature, physical property, and flow rate variations across the column. Additionally, some new correlations for the physical properties of the hydrocarbon compounds (aromatics and saturated) were developed. The accuracy of the mathematical model is checked with randomly selected field data of an industrial plant. The results show that the average error of the model in predicting the performance of the RDC is less than 10%. A parametric study of the extraction of aromatic compounds from a lube-oil cut, carried out in a RDC column, reveals that with increasing the solvent-to-feed 9431



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ratio, rotor diameter, disk rotation rate, and both feed and solvent temperatures, the extraction yield can be increased.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +1 303-556-2370. E-mail: arunprakash.karunanithi@ ucdenver.edu. Notes

The authors declare no competing financial interest.

■

a C̅

C CA CN CP Cp Na Q V V̅ W x y

NOTATIONS special mass-transfer area (m2/m3) mass concentration of the components in the continuous phase (kg/m3) mass concentration of the components in the dispersed phase (kg/m3) aromatics concentration (%) naphthenic concentration (%) paraffinic concentration (%) mass heat capacity (kJ/kg·K) mass-transfer rate (kg/s) volumetric flow rate (m3/h) volume of the compartment (m3) component molar volume (cm3/g·mol) mass flow rate (kg/s) component mole fraction component mass fraction

Subscript

a c d E f i n N ref s

aromatics continuous phase dispersed phase extract furfural component counter number of compartments reference saturated component

Superscript

* equilibrium condition

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REFERENCES

(1) Singh, H.; Kishore, K. Solvent refining of medium viscosity distillate and changes in group chemical composition. J. Appl. Chem. Biotechnol. 1978, 28, 617−625. (2) Vakili-Nezhad, G. R.; Modares, H.; Mansoori, G. A. Solvent extraction of aromatic components from lube-oil cut by Nmethylpyrrolidone (NMP). Chem. Eng. Technol. 1999, 22, 847−853. (3) Coto, B.; van Grieken, R.; Pena, J. L.; Espada, J. J. A model to predict physical properties for light lubricating oils and its application to the extraction process by furfural. Chem. Eng. Sci. 2006, 61, 4381− 4392. (4) Meindersma, G. W.; van Schoonhoven, T.; Kuzmanovic, B.; de Haan, A. B. Extraction of toluene, o-xylene from heptane and benzyl alcohol from toluenewith aqueous cyclodextrins. Chem. Eng. Process 2006, 45, 175−183. (5) Domanska, U.; Pobudkowska, A.; Krolikowski, M. Separation of aromatic hydrocarbons from alkanes using ionic liquid C2NTf2 at T = 298.15 K. Fluid Phase Equilib. 2007, 259, 173−179. (6) Marple, S.; Train, K. E.; Foster, F. D. Deasphalting in a rotating disc contactor. Chem. Eng. Prog. 1961, 57, 44−48. (7) Reman, G. H.; Olney, R. B. The rotating disc contactor: new tool for liquid−liquid extraction. Chem. Eng. Prog. 1955, 51, 141−146. 9432


Modeling and Simulation of a Rotating-Disk Contactor for the

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