CFD modeling to predict diffused date syrup yield and quality from sugar production process

Journal of Food Engineering 118 (2013) 205–212

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CFD modeling to predict diffused date syrup yield and quality from sugar production process Karim Gabsi a,1, Maher Trigui a,⇑, Ahmed Noureddine Helal b,2, Suzelle Barrington c,3, Ali R. Taherian a,⇑ a

Unité de recherche Génome, Diagnostic immunitaire et Valorisation, Institut Supérieur de Biotechnologie de Monastir, Université de Monastir, Monastir, Tunisia Université de Sousse, Rue Khalifa El Karoui, Sahloul-BP n°526_4002, Sousse, Tunisia c Department of Bioresource Engineering, Macdonald Campus of McGill University, 21 111 Lakeshore, MS1025, Ste Anne de Bellevue, Quebec, Canada H9X 3V9 b

a r t i c l e

i n f o

Article history: Received 21 May 2012 Received in revised form 20 December 2012 Accepted 15 April 2013 Available online 25 April 2013 Keywords: Date Sugar Mass transfer Computational fluids dynamics (CFD)

a b s t r a c t In this study, diffusion process of sugar from date is modeled using a commercial computational fluids dynamics (CFD) code FLUENT 6.3.23 (Fluent Inc., USA). A two phases CFD model was developed using an Eulerian–Eulerian approach to calculate the date volume fraction transferred during time from date phase to water phase. The diffusion process was studied as function of three date varieties (Manakher, Lemsi and Alligue), three speeds of agitation (0, 50 and 100 rpm) and three date/water ratio (0.25, 0.50 and 0.75). The results revealed that, for mass transfer, the numerical data were in good agreement with the experimental data indicating the R2 of 0.84. Using a Lemsi date variety, the optimal condition of diffusion were 50 rpm and 0.75 for speed of agitation and date/water ratio respectively. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Sugar is the basic food carbohydrate, it is important to the structure of many foods including biscuits and cookies, cakes and pies, candy, ice cream and sorbets (Gibney et al., 1995; Izydorczyk, 2005). The source of sugar in Tunisia is mainly from the beet with a production of 20,700 tons in 2004 (I.N.S, 2004) and consumption of 30,800 tons in the same year (Sugar Year Book, 2002). The noticeable difference between production and consumption in Tunisia and the other parts of the world rises seeking alternative sources for sugar. For instance, in Spain, extraction and purification techniques of sugar from carob was the subject of study of Petit and Pinilla (1995). In Indonesia Pontoh and Low (1995) extracted glucose syrup from Indonesian palm and cassava starch. In Brazil Azevedo and Rodrigues (2000) produced fructose with a purity of 90% from cashew apple juice using chromatography process. D’Egidio et al. (1998) obtained fructose from cereal stems and polyannual cultures of Jerusalem artichoke. However, sugars are the most important element of date pulp and account for 44–88.6% of the dry-weight. The mass of non-consumed ⇑ Corresponding authors. Tel.: +216 73 465 405, +216 98 606 215; fax: +216 73 465 404 (M. Trigui), tel.: +1 450 768 3329; fax: +1 514 624 2945 (A.R. Taherian). E-mail addresses: [email protected] (M. Trigui), [email protected] (A.N. Helal), [email protected] (S. Barrington), [email protected] (A.R. Taherian). 1 Tel.: +216 73 465 405; fax +216 73 465 404. 2 Tel.: +216 73 368 130; fax: +216 73 368 126. 3 Tel.: +1 514 398 7776; fax: +1 514 398 8387. 0260-8774/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2013.04.011

dates produced in Tunisia is estimated to be 43,300 tonnes per year. These quantity of date could produce a mass of 30,000 tonnes of sugar (Rhouma, 1994; C.R.D.A, 2006). Study by Saafi et al. (2008) on the mixture of low quality date (Khalti) from the South-Eastern of Tunisia showed that the date pulp contains 51.66% reducing sugars (glucose and fructose) and 6.63% sucrose on the dry-weight basis. A sugar extraction procedure from date is a complex process. Therefore, it is impossible to run a plant by trial and error to find out a set of operating parameters, because a large number of parameter involved in the process. The principle of extraction of sugar from date is based on mass transfer of sugar from date phase to water phase. As reported by Datta (2007), in food systems, the extraction processes can be viewed as involving transport of heat and mass through porous media. For the purpose of modeling transport processes in food systems, we can divide a porous media into two general groups, one involving large pores, and the other, small pores. In the large pores, fluid flow is mostly outside of the solid. An example of this is in cooling of stacked bulk produce such as oranges and strawberries. The fluid flow in this case is through the empty spaces of these stacked systems and is treated as a Navier–Stokes analog that is a generalization of Darcy flow. The other group consists of situations where the flow is inside the solid (pores are small). Example of this includes moisture transport inside the solid of many food processes such as drying, frying and microwave heating. Here the fluid transport through the pores of the solid is treated in terms of the simplest version of Darcy flow as opposed to its generalization into a

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Nomenclature

aq

~ vq _ pq m _ qp m Sq q

l ls lt k s w ~ ns Pw Pc P Ds

qs M Ds,m DT,s Cs

the phase volume fraction the velocity of q phase the mass transfer from the pth to qth phase the mass transfer from phase q to p phase the source term the flux the viscosity the sugar viscosity the eddy viscosity the permeability sugar phase water phase the total flux of sugar the water pressure the capillary pressure of gaz phase the gaz pressure the capillary diffusivity of sugar the density the mole fraction of mixture the mass diffusion coefficient for sugar in the mixture the thermal diffusion coefficient the sugar concentration

Navier–Stokes analog, as mentioned for the other group. Several authors have proposed modeling procedures for assessing heat and mass transfers in food system (Datta, 2007). For example, Chourasia and Goswami (2007) developed a CFD model for the heat and mass transfer and moisture loss in the stack of bagged potatoes. The model was able to reflect the evolution of both product temperature and moisture loss as function of many parameters such as, the porosity and the temperature. A similar approach was taken to study the heat and water transfers of stacked food products placed in airflow (Le Page et al., 2009). This study reports on the development of an modeling procedure combining experimental correlations for the heat and mass transfer coefficient determination and specific user-defined functions (UDFs) implemented in the commercial CFD code Fluent to simulate the interrelationships at play between airflow and transfers of unwrapped food products bathing in water. Therefore, the main objective of this project was to generate and validate a CFD model in order to predict the yield and the quality parameters related to the purity of extracted sugar as a function of the following factors:

Sct Dt hs ~ Ss E Es Ef keff

the the the the the the the the the

Shf

the fluid enthalpy source term

f

the the the the the the the the the the the

c

sp Re C

as,w as,d c s ga m n

effective Schmidt number effective mass diffusion coefficient specific enthalpy of the sugar phase heat flux energy total solid energy total fluid energy porosity effective thermal conductivity drag function particulate relaxation time relative Reynolds number model parameter volume fraction of sugar from the water phase volume fraction of sugar of date phase shear rate shear stress apparent viscosity consistency coefficient flow behavior index

by a 45° pitched blade impeller with four blades mounted on 10 mm diameter shaft placed in the centerline of the working volume and 100 mm from head plate of the vessel. The mass of date pulp was crushed in homogenous paste, placed in reactor and then immersed with the appropriate volume of water. The diffusion process took 3 h at fixed temperature of 80 °C. The sugar content of all samples was then measured by HPLC assay. The pulp was agitated using a blade impeller with velocities ranging from 0 to 100 rpm and selected levels of solid:liquid ratios from 0.25 to 0.75 (Table 1). 2.2. Experimental design Response Surface methodology, an empirical modelization technique devoted to estimate interaction and quadratic effects, was employed to find improved or optimal process settings, troubleshooting, and weak points. The optimization of sugar diffusion process from date involved three major steps of performing the statistically designed

(a) sugar diffusivity from date pulp as an intrinsic parameters of fruit material, (b) agitation parameters of process, and (c) date:water ratio.

2. Materials and methods 2.1. Experimental setup Three varieties of dates including Menakher, Lemsi and Alligue with different coefficients of sugar diffusivity were obtained from local market. The differences in coefficients of sugar diffusivity are due to the dissimilarity of the date texture as stated by Trigui et al. (2011). A laboratory scale apparatus was designed to conduct the experiments (Fig. 1). The apparatus consists of 2L bioreactor with 1L working volume and reactor is equipped with automatic feedback controllers for temperature and mixing. The mixing is driven

Fig. 1. Graphical illustration of solution domain.

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experiments, estimating the coefficients in a mathematical model, predicting the response and checking the adequacy of the model. Box–Behnken was selected as experimental design for this study. Sugar diffusivity, agitation, and date:water ratio were considered as significant input variables and designated as X1, X2 and X3 respectively. The sugar concentration is considered as the output variable which is measured at the end of each run. The low, middle, and high levels of each input variable designated as , 0, and + are given in Table 2 and experimental design is tabulated in Table 3.

Table 2 Process factors and their levels used to study diffusion process of sugar from date.

2.3. Analytical procedure

Table 3 The design of experiments.

Assessments of sugar contents for all samples were performed by HPLC. The sample of date syrup was analyzed by injection in a chromatographic ion-exchange column equipped with a refractive index detector. The analysis parameters were: – Column: SUPEL COSIL LC-NH2, 25 cm  4.6 mm I.D., 5 lm particles. – Mobile phase: acetonitrile:water (75:25) – Flow rate: 1 ml/min. – Injection: 10 ll, 150 lg each sugar. 2.4. CFD modeling 2.4.1. Description of the model The extraction of sugar from date occurs as transport through porous media (Datta, 2007). The diffusion of sugar is due to capillarity, concentration gradient, temperature gradient or combination of these factors. In intense heating, pressure driven flow due to the internal evaporation which can be dominant effect (Ni et al., 1999). The process of sugar extraction is assumed to a diffusion mechanism in which water replace the date syrup and via counter current of two phases. The Eulerian two-phases was used to model sugar-water flow. The properties of two phases are given in Table 1.

Factor

Levels 

0

+

Date variety Agitation (rpm) Date/water ratio

Menakher 0 0.25

Alligue 50 0.5

Lemsi 100 0.75

Runs

Sugar diffusivity (cm2/s)

Agitation (rpm)

Date/water ratio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Menakher Lemsi Alligue Menakher Alligue Alligue Alligue Alligue Menakher Alligue Alligue Lemsi Lemsi Menakher Lemsi

50 100 50 50 50 100 0 0 100 100 50 50 50 0 0

0.75 0.50 0.50 0.25 0.50 0.25 0.25 0.75 0.50 0.75 0.50 0.75 0.25 0.50 0.50

where ~ v q is the velocity of q phase and m_ pq characterizes the mass _ qp characterizes the mass transfer from the pth to qth phase, and m transfer from phase q to p phase, and Sq is the source term. 2.4.4. Conservation of momentum 2.4.4.1. General model. In porous media the general momentum equation is given by the Darcy law:

q¼ 2.4.2. Governing equations with assumptions The fitted equations for this approach can be derived by ensemble averaging the fundamental conservation equations for each phase to describe the motion of sugar and water.

k

l

rP

where q is the flux, k is the permeability of the matrix, l is the viscosity and rP is the pressure gradient vector The total flux of sugar, ~ ns , are composed of convective of Darcy flow and diffusion respectively:

2.4.3. Conservation of mass The description of multiphase flows as interpenetrating continua incorporates the concept of phase volume fraction (aq). The volume fraction of each phase is calculated from a continuity equation: n X @ ðaq qq Þ þ rðaq qq ~ v q Þ ¼ ðm_ pq  m_ qp Þ þ Sq @t p¼1

ð2Þ

ð3Þ

ð1Þ

Table 1 Properties of two phases. System properties

Value/expression

Units

Date syrup Viscosity Reference temperature Characteristic viscosity Parameter for shear rate, n Specific heat (Cp) Thermal conductivity (k) Density

mcn1 298.11 0.012 1.561 3280 0.0454 1.08

K kg/ms – J/kg K W/m K kg/m3

Water Specific heat (Cp) Standard state enthalpy Reference temperature

4182 2.85  108 298.11

J/kg K J/kg mol K

@C s þ r  ð~ ns Þ ¼ I_ @t

ð4Þ

@C w þ r  ð~ nw Þ ¼ I_ @t

ð5Þ

In low temperature, capillarity is the primary mode of species transport and variation in temperature can be ignored and no significant evaporation ðI_ ¼ 0Þ

@C s þ r  ð~ ns Þ ¼ 0 @t ks ~ ns ¼ qs rPw

ls

~ ns ¼ qs

ks

ls

rðP  Pc Þ

ð6Þ ð7Þ ð8Þ

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where Pw is the water pressure, P is the gaz pressure and Pc is the gaz capillary pressure. In the absence of intense heating, the pressure inside the material stays at atmospheric conditions, thus Pc  P, Eq. (8) can be written as:

~ ns ¼ qs

ks

ls

rP c

ð9Þ

Eq. (9) can be rewritten as:





@C s ks qs g þ r  qs rh ¼ 0 @t ls

ð10Þ

Thus this equation can be written as:

@C s  r  ðDs rC s Þ ¼ 0 @t

ð11Þ

where Ds stands for the capillary diffusivity of sugar given by:

Ds ¼ q2s

ks g @h ls @C s

ð12Þ

Unlike the intense heating and in a laminar flow, due to combined effect of concentration gradient and temperature gradient from saturated to unsaturated the flux of sugar flows:

C s ¼ qs  M Ds;m rC s ¼ Ds:m rðqs MÞ

ð13Þ ð14Þ

Ds;m rC s ¼ qs Ds;m rM

ð15Þ

~ ns ¼ qs Ds;m rM  DT;s

rT T

1  Cs ¼ P Cw

ð17Þ

ð21Þ

where Ef is the total fluid energy, Es the total solid medium energy, c the porosity, keff the effective thermal conductivity and Shf the fluid enthalpy source term. 2.4.6. Interfacial momentum exchange The most important inter-phase force is the drag force acting on the bubbles which resulted from the mean relative velocity between the two phases and an additional contribution resulting from turbulent fluctuations in the volume fraction due to the averaging of the momentum equations (FLUENT 6.3, 2006). Other forces such as lift and added mass force may also be significant under the velocity gradient of the surrounding liquid and acceleration of bubbles respectively. These forces and the turbulent fluctuation of the volume fraction in the drag force were not been included in this paper. The exchange coefficient is given by the following equation:

as aw qw f sp

K sw ¼

ð22Þ

where f, the drag function is defined differently for the different exchange-coefficient models (as described below) and sp, the ‘‘particulate relaxation time’’, is defined as:

sp ¼

ð16Þ

where M is the mole fraction of mixture (sugar and water), Ds,m and DT,s are the mass diffusion coefficient for sugar in the mixture and the thermal diffusion coefficient respectively. Equation (13) is strictly valid when the mixture composition is not changing, or when Ds,m is independent of composition. This is an acceptable approximation in dilute mixtures when Cs  1.

Ds;m

@ ðcqf Ef þ ð1  cÞqs Es Þ þ r  ð~ v ðqf Ef þ pÞÞ @t ~ Ss Þ þ ð s ¼ r  ½keff rT  ðRhs~ v Þ þ Shf

qw d2w 18ls

ð23Þ

For calculation of the drag coefficient, the standard correlation of Schiller and Naumann is used (Ishii and Zuber, 1979):

f ¼

C D Re 24

ð24Þ

where

( CD ¼

24ð1þ0:15Re0:687 Þ Re

Re 6 1000

0:44

Re > 1000

ð25Þ

Ds

Due to the combined effect of concentration gradient and temperature gradient from saturated to unsaturated flow, the transfer of sugar with intense heating and agitation is considered as turbulent flow and Eq. (13) is replaced by the following form:

 ~ ns ¼  qs Ds;m þ

lt Sct



rM  DT;s

rT T

ð18Þ

where lt is the eddy viscosity and Sct is the effective Schmidt number for the turbulent flow:

Sct ¼

lt qs Dt

ð19Þ

Dt is the effective mass diffusion coefficient due to turbulence. 2.4.5. Conservation of energy The conservation of energy is described by the following equation:

X @ ðqEÞ þ r  ð~ v ðqE þ pÞÞ ¼ r  ðkeff rT  hs~Ss þ ðseff  ~ v ÞÞ @t ð20Þ where hs is the specific enthalpy of the sugar phase (s) and ~ Ss is the heat flux. In the porous media, the conduction flux uses an effective conductivity and the transient term includes the thermal inertia of the solid region on the medium:

and Re is the relative Reynolds number. The relative Reynolds number for the water phase (w) and sugar phase (s) is obtained from:

Re ¼

qs j~ vw  ~ v s jdw ls

ð26Þ

However, this basic drag correlation applies to the bubbles moving in a still liquid and not to the bubbles moving in turbulent liquid. In this work, a modified drag law which considers the effect of turbulence is used. It is based on a modified viscosity term in the relative Reynolds number (Bakker and Van den Akker, 1994):

Re ¼

qs j~ v w  ~sjdw ls  C lt;s

ð27Þ

where C is the model parameter which consider the effect of turbulence in reducing slip velocity. 2.4.6.1. Initial and boundary conditions. The tank includes three fluid zones representing the impeller region, the region where the dates are initially located, and the water phase region. There are no conditions to be specified for the latter two zones, hence, conditions only in the zone representing the impeller should be set. The impeller is considered solid moving mesh and defines the value of angular velocity (0, 50 or 100 rpm) that simulates the impeller. The condition was specified for date and water separately using UDF. The walls of the tank are kept at 80 °C with no slip condition applied with the specified temperature.

K. Gabsi et al. / Journal of Food Engineering 118 (2013) 205–212 

T ¼ T wall ¼ 80 C;

V r ¼ 0;

209

Vz ¼ 0

for 0 6 z 6 H at r = R. The axisymmetry conditions were applied for the simulation and segment of the geometry was taken for analysis in order to save on computation time. The initial value of volume fraction of sugar from the phase of water (as,w) is:

as;w ¼ 0

t ¼ 0;

The initial value for volume fraction of sugar from the date phase (as,d) depends on the variety of date studied: Menakher variety: t = 0, as,d = 0.54. Lemsi variety: t = 0, as,d = 0.58. Alligue variety: t = 0, as,d = 0.80.

2.4.6.2. Rate of mass transfer of sugar. In this paper, the coefficient of diffusivity of sugar from date to water is calculated based on the modular feed forward networks model (Trigui et al., 2011). A user-defined function (UDF) is used to read the coefficient of diffusivity for sugar from the output file of the modular feed forward networks model.

Fig. 2. Unstructured mesh used in the model.

2.4.6.3. Phase properties. Table 1 shows the value and expression of properties for the phase of water and date. The expression and values of viscosity parameters for date syrup was determined using rheological model of date syrup. Brookfield rotational viscometer (Model RVDV-II, Brookfield Engineering Inc., USA) equipped with spindle model RV7 was used. Enough samples in a 600 mL beaker were used to immerse the groove on the spindle with guard leg. The flow behavior of four date syrup solutions, having a concentrations 17, 24, 31 and 39 Brix respectively, was determined at 20, 40, 60 and 80 °C as forward measurement (speed increasing) and also as backward measurement (speed decreasing). Temperature was maintained using thermostatically controlled water bath. Shear rate and shear stress were calculated using the apparent viscosity and speed (rpm) in the following equations:

c ¼ 0:209  N s ¼ ga c

ð28Þ ð29Þ

where ga is the apparent viscosity (Pa s), N is the rotational speed (rpm), s is the shear stress (Pa), and c is the shear rate (s1). The power law model described flow behavior: n

s ¼ mc

ð30Þ n

where m (Pa s ) is the consistency coefficient, n (dimensionless) is the flow behavior index (Habibi-Najafi and Alaei, 2006). 2.4.6.4. 4-Numerical method. CFD simulations were conducted based on the above mathematical analysis and since the employed tank was symmetrical, a two dimensional model was developed. By using Gambit 2.2.30 software, a quadratic map grid of 3876 cells was employed to resolve the species mass fraction, velocity, temperature and pressure gradients in the boundary layer and within the food, induced by the heating, diffusion and redirection of flow. The unstructured mesh used in the model was presented in Fig. 2. The Fluent 6.3 software was used to resolve these equations. The residuals were kept to 1  103 for all variables and the time step was kept small to 103 s to ensure stability. Execution time for t = 300 s elapsed time was approximately 60s on a Pentium 4 with two processor element, 3.02 GHz and 1 GB RAM machine running windows XP professional.

Fig. 3. Correlation of experimental versus predicted values of date volume fraction after 900 s of reaction time.

2.4.7. Validation The procedures for the current study were validated by comparing the variation of midpoint volume fraction of date within the time in a tank with experimental results (Fig. 3). In addition, the volume fraction of date contours plots was also found to be nearly identical for the duration of diffusion.

3. Results and discussion 3.1. Validation The comparison between the experimental and predicted date volume fraction obtained after 900 s of diffusion reaction, for 15 runs, is shown in Fig. 3. It can be seen that the simulation data is in excellent agreement with the experimental data. The correlation coefficient for the predicted and experimental date also showed a good agreement for the volume fraction (R2 = 0.84). This suggests that the diffusion process of sugar from date can be accurately predicted by the CFD model.

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3.2. Contour of date volume fraction Fig. 4 illustrate the time evolution of date volume fraction inside the reactor. Three forces direct the movement of molecules: the gravity force, the rotational force and the diffusion rate. The sugar diffuse from date phase to water phase and the water replaces the date syrup by counter current. Initially, the phase 1 was mostly filled with water and phase 2 was more concentrated in sugars. Over time, the fluids flowed from the bottom upwards due to the rotational and gravitational forces. Also the volume fraction of date decreased at the date phase and increased in water phase by the mass transfer reaction. Fig. 5 shows the change at the date volume fraction distribution as a result of the combination effect of the

diffusion rate for each variety, the angular velocity of impeller and the date/water ratio during 15 min. The simulation started with case 1, where the angular velocity fixed at 50 rpm and the date phase corresponds to the Menakher variety. Although identical conditions are applied in case 4 and the contours profile of the two cases are different, the rate of diffusion in case 4 is smaller than that of case 1. This difference could be due to the dissimilarity of date:water ratio used (0.25 < 0.75). For the cases 2 and 9, the angular velocity is fixed at 100 rpm and similar date:water ratio (0.5) was employed. The contour of date volume fraction shows also different rate of diffusion due to the dissimilarity of varieties. As mentioned earlier, the difference in coefficients of sugar diffusivity is related to the difference in

Fig. 4. Time evolution of date volume fraction in 2D reactor.

Fig. 5. Contours of date volume fraction of 15 cases after 900 s.

K. Gabsi et al. / Journal of Food Engineering 118 (2013) 205–212

211

Fig. 7. The date volume fraction versus the runs after 900 s of reaction time.

texture of date’s varieties (Trigui et al., 2011). It is also worth mentioned that any increase in diffusion flow rate could increase the diffusion time. In the cases 6 and 7, the Alligue variety was used and the date:water ratio kept fixed at 0.25. The diffusion rate increased with raising the angular velocity of impeller which was identical to the contour profiles of both cases 9 (100 rpm) and 14 (0 rpm). Impeller speed is a very important parameter which affects the velocity and diffusion time in a stirring tank and, apparently, increasing impeller speed could reduce the mixing time. Increase in impeller speed reinforced the degree of turbulent intensity and the liquid circulation speed augmented and caused the reduction of the mixing time in the stirring tank. 3.3. Optimal operating conditions The diffusion of sugar from date was studied as a function of date variety, agitation and the date:water ratio. As shown in Fig. 6a–c, the highest value for date volume fraction was obtained when using the Lemsi variety, as well as, the date:water ratio and agitation speed were larger than 0.6 and more than 40 rpm respectively. Fig. 7 represent the runs versus the date volume fraction. The run 12 shows the optimal condition for diffusion of sugar from date where the value of date volume fraction obtained after 900s was 0.36. In this run, the diffusion process encountered an agitation speed of 50 rpm (>40 rpm), date:water ratio of 0.75 (>0.7) and the Lemsi date variety with the highest sugar diffusivity coefficient (Trigui et al., 2011). For the run 10 the diffusion process involved the agitation speed of 100 rpm, date:water ratio of 0.75, the date variety of Alligue, and the date volume fraction of 0.25. 4. Conclusion

Fig. 6. Evolution of date volume fraction as function of operating conditions after 900 s of reaction time: (a) the volume fraction versus date/water ratio and agitation, (b) the volume fraction versus date/water ratio and variety of date, and (c) the date volume fraction versus agitation and variety of date.

A CFD model of date-water diffusion in agitated vessel was used to predict mass transfer. The model predicted the sugar mass transfer from date to water as the function of impeller speed, date:water ratio and the varieties of date. The numerical results were compared with the experimental data for mass transfer which

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indicated a good agreement. The optimal condition of diffusion was obtained by applying an agitation speed of 50 rpm, date:water ratio of 0.75 when using a Lemsi date variety. The determination of optimal condition for diffusion of sugar from date in batch process was used to develop the model for a continuous process regarding production of sugars from date in the future works.

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