Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤١٣ DEVELOPING CORRELATION FOR PREDICTION OF GAS HOLDUP USING GENETIC ALGORITHM Dr. Salih Abdul Jabbar Salih College of Engineering Al-Qadisiya University Abstract: This paper deals with the prediction of the overall gas holdup �g in slurry bubble column depending on wide range of databank of around 69 measurements collected from the open literature. Correlation for gas holdup was derived using combination of dimensionless analysis and Genetic Algorithm. The correlation takes in consideration the physical properties of liquid and gas that effect on gas holdup and therefore effect on the design of slurry bubble column. Also a comparison between the correlation driven from Genetic Algorithm and a new correlation driven using Quasi-Newton method was made and found that the Average Absolute Relative Error (AARE) was 10.8 % and 16.1%, respectively. This shows that the use of Genetic Algorithm is improve the prediction of gas holdup in slurry bubble column. Key Word: Genetic Algorithm, gas holdup, slurry bubble column. ���� ��� �� ����� ��� ا��! �� ا���زي ������ام ا���ارز��� ا���� � ا��آ��ر #��" ��� ا����ر #��" ��� آ��� ا�% (��)� ا�'�د��� :ا���#� ��� � ا ��� � ��� ا ��ز �� �� � ه�ا ا���� !�"� �g ��� ا ! اغ إ #$ # �+ط ��(" �&�د "'&� �&%ا ا !0/. ذو ا ٦٩" 3&&� �4 �&&4 3&&/'� %>&&3 ا;د�/&&�ت &&9 ا8&& 7 ا�56 � �/&&3 ا'� &&9 @&&+ل <وا6&&3 . ا �&&�� 5&&�ا ا 3&&<+" �4&&� ا �&&A%ل "'&& /3 ا 7%ارز /3 ا C%ر�3 %D /E �/ �� � . و&'" FG&4 #& ��@� ه�ا ا ��� ��K ا(" ��ر ا 7%اص ا !/<��و�&3 '�&�ز وا &�H�I وا � ��� ا ! اغ � ��� ا ��ز ا�� �g FG4 # �!�"� وا �/� ه�ا ا �%ع 9 اA4 �'" M�� �� �0رO&3 �&/9 ه&�ا ا ��&� إ6& اء 4&� . $/ Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤١٤ ��0رO&3 ه&% ه&�X "+>&3 ر��W&/3 وآ�O V&O ��U 3&�/&�د O/&%94 -آ/%8&# 30 � �4 ا �A%ل "'/R �%ا3C8 ا8 M7ام D أ@ و�/9 ���4 ا Y ا8 M7ام �A � ا>� ه�CX �30 ا 7%ارز /3 ا C%ر�V'A� �/� 3 ا'" 30� C �Mل @�C ا)0&3 %) ١٠.٣� C ا;@& ى 9 ا Mىاوه� %). ١٦.١( 3 ��/9/� . ا8 M7ام D �30 ا 7%ارز /3 ا C%ر�3أه Symbols used a, b ,c, d, e and z Constants. Ar Archimedes number, Ca Capillary no., , Cs volumetric solid concentration, vol %, db Gas bubble diameter, m, Eo Eotvos number, Fr Froude number, Mo Morton number, R The cross-correlation coefficient, Re Reynolds no., , Ug gas velocity, m/s, g ε Gas holdup, g ρ Gas density, kg/m3, g µ Gas viscosity, Pa.s, L ρ Liquid density, kg/m 3 , L σ Liquid surface tension, N/m, L µ Liquid viscosity, Pa.s, Introduction Slurry bubble column are widely used in chemical, biochemical, fuel and environmental engineering, and many industries. The use of slurry bubble column in industries is due to their simple construction, low operating cost and high – energy efficiency. Major important technology figures prominently in processes for converting natural gas to liquid fuels and light olefins using Fisher –Tropsch synthesis (Albijanic et.al. 2006). Bubble columns are an attractive reactors for various multiphase processes, especially for processes involving highly exothermic reactions. These reactors are operated in semi-batched or continuous mode. For this reason, the Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤١٥ hydrodynamics of such reactors are controlled mainly by the gas flow. Overall gas holdup is one of the important parameter for slurry bubble column design and scale up. It is defined as the fraction of the reactor dynamic volume occupied by the gas (Mouza et. al. 2005). The behavior of gas holdup has been attributed to many different factors, including the physical properties of gas/liquid/solid phase, gas velocity, and solid loading (Shah, 1979). Albijanic et. al. (2006), studied the gas holdup in slurry bubble column reactor operated with diluted solution of alcohols and developed a correlation depends on physical properties of liquid such as viscosity and density and surface tension. Ruthiya (2005) studied the gas holdup in slurry bubble column especially the influence of particles on gas holdup and found that the rate of decrease of gas holdup with increasing slurry concentration in the heterogeneous regime lower compared to the rate of decrease of gas holdup in the transition regime. Mouza et. al.(2005) gave a new correlation based on dimensionless groups(Fr, Ar and Eo) for the prediction of gas holdup in the homogeneous regain. Also he found that the viscosity have an influence on bubble coalescence and hinders breakage. Also he found that an increasing of surface tension increase bubble formation by promoting breakage and demoting coalescence. Shaikh et. al. (2003) studied the gas holdup in slurry bubble column and gave a correlation using Artificial Neural Network to predict the gas holdup using dimensionless groups (Re, Fr, Eo, and Mo). The correlation has the lowest AARE when they compared to selected correlations. Ruzicka et.al. (2003) studied the effect of viscosity on gas holdup, and found that the gas holdup decrease with increasing viscosity. Vendu and Krishna (2003) studied gas holdup in slurry bubble column for air/ethanol system with three different concentrations. They found that the increasing of solid concentration tends to decrease gas holdup. This decrease due to the increase of coalescence of small bubbles to form larger bubbles. Shirsat et. al. (2003) observed that as the effective column height increases, the gas holdup also increases due to the increase in the residence time of the bubbles in the contactor. Michele et. al. (2000) used CFD method to predict gas holdup depending on superficial gas velocity solid loading and sparger geometry. DeSwart et.al. (1996) studied the hydrodynamics of slurry bubble columns, and found that increasing slurry concentration reduces the total gas holdup and this reduction is to be largely attributed to the destruction of the small bubble population which have bubble diameters smallest than 10 mm. Increasing slurry concentration increases the size and distribution of the large bubbles. Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤١٦ Artificial techniques brought a new sight to the characterization of gas holdup in slurry bubble column. To the best of our knowledge, the pioneer of the use of these techniques is Shaikh et.al.(2003) and Behkish (2004), both authors used back propagation neural network for prediction of gas holdup. However, correlations still keep the lock of experimental data. Proper functions require significant computational effort when they are nonlinear and involve large number of parameters. For this reason, Genetic Algorithms bring efficient solutions by avoiding local minima. Moreover, it improves the robustness toward the uncertainties on the correlation coefficients, due to their adaptive and stochastic aspects. The main object of this study is to predicate the gas holdup using the Genetic Algorithm techniques which is done using Statistica 7 from StatSoft, Inc., and a comparison between the above correlation and another correlation done using another method (Quasi- Newton) was done. Genetic Algorithms Genetic algorithm is a particular class of evolutionary algorithms, which are adaptive search techniques for approximating solutions of optimization and prediction problems. They are based on a biological metaphor which simulates processes in natural systems that are necessary for evolution, specifically those that follow the principles first proposed by Charles Darwin of the survival of the fittest. As such, they represent an intelligent exploitation of a random search within a defined search space to solve a problem. A population of abstract representations (chromosomes) of solution candidates (individuals) for an optimization problem evolves toward better solutions. Traditionally, solutions are represented in binary systems as an array of bits, but different encodings are also possible, such as integer or real encodings. The evolution begins from a population of completely random individuals (initialization) and happens in generations. In each generation, the fitness of the whole population is evaluated. Multiple individuals are stochastically selected (selection) from the current population according to their fitness, and mutated (mutation) or recombined (crossover) to form a new population (reproduction). The latter is then used in the next iteration. The algorithm stops when a solution is found satisfying minimum criteria or when a fixed number of iterations are reached. When applying genetic algorithm, one has to define at least a genetic representation of the solution domain (encoding) and at the same time a fitness function to evaluate the defined solution domain. In other words, Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤١٧ one needs to fix the encoding of the solution as an array of bits, integers or floats in such a way that their parts are easily aligned due to their fixed size. Besides, at the encoding stage, one has to take into account the crossover and mutation operator complexity, which depends on the solution representation. Indeed, in some situations, in addition to problems associated with encoding and with evaluation definitions, one can face the problem of the definition of crossover and mutation operators in order to keep the validity of the solution. Furthermore, the fitness function has to be defined over the genetic representation in order to measure the quality of the represented solution. The fitness function is always problem dependent (Melanie, 1998). Once the genetic representation of the solution is known and the corresponding fitness function is defined, the genetic algorithm starts initializing a population of solutions randomly. Then the algorithm improves it by repetitive applications of crossover, mutation and selection operators Figure (1). 1. Collection of Data A set of 69 experimental data of different systems were collected from literatures for different workers. The data collected for slurry bubble column reactor operated with different liquids and different slurry concentration. Table (1) summarizes the sources of data. The physical properties such as density, surface tension and viscosity were included in the data base. Most of slurry bubble column are operated with low liquid velocities, which have been reported to have little or no effect on over all gas holdup (Shetty et. al. 1992), so it is not included in the correlation. 2. Dimensionless Groups Most of workers on slurry bubble column reactors predicted the gas holdup using correlations based on dimensionless groups. The following criteria guide was used to choose the input dimensionless groups: a. The dimensionless groups should be as few as possible. b. Each group should be highly cross-correlated to the output parameter. c. The input groups should be weakly cross-correlated to each other. Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤١٨ So in this study Reynolds number, densities of gas to liquid ratio, viscosities of gas to liquid ratio, volumetric solid concentration, and finally the Capillary number (which were used by (Hikita et. al., 1988) and (Zou et. al., 1988)), where used to predict gas holdup in our work. 3. Statistical Analysis The statistical analysis of prediction results is based on the following criteria: a. The average absolute relative error (ARRE) should be minimum. ∑ − = N pred y yy N AARE 1 .exp .exp.1 1 b. The cross-correlation coefficient, R between input and output should be around unity. ( ) ( ) ( ) ( )∑∑ ∑ −− −−− = N meanpredpred N mean N meanpredpredmean yyyy yyyy R 1 2 ).(. 1 2 ).(exp.exp 1 ).(.).(exp.exp 2 Results and Desiccation a. Gas holdup Prediction Using Genetic Algorithm Using the Statistica Neural Network 7 (SNN) a correlation has been developed to predicate the gas holdup by applying the 69 experimental data point collected (section 4), putting the population at 100, generations at 100 and mutation rate at 0.1 as shown in Figure (2). Table (2) shows the minimum and maximum of dimensionless groups used. Table (3) shows the model summary used to predict the gas holdup using SNN. The final predicted gas holdup has been drawn against the experimental gas holdup Figure (3). b. Gas holdup Prediction Using Quasi- Newton Method Using the Statistica 99 and Quasi-Newton method (QN) a correlation has developed to predicate the gas holdup by applying the 69 experimental data point collected using the following form: ze d L g c L gb g a CaCvRe ++      +      ++= µ µ ρ ρ ε 3 The result from the program is shown below Table (4). Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤١٩ The equation 3 will be: 015.00189.0 189.0168.0 0837.0 CaCvRe09.6 −− − ++      +      ++−= L g L g g µ µ ρ ρ ε 4 Figure (4) shows the relation between the experimental and predicated gas holdup using the QN method. Comparing between the correlations obtained using SNN and QN are shown in Figure (5), which leads to conclude that Genetic Algorithm is more accurate than Quasi-Newton method. Moreover the comparing between these correlations on statistical analysis basis leads to above the conclusions. Table (5) shows the mentioned comparing. Conclusions In this paper, a new presentation of predicating gas holdup in slurry bubble column was made using Genetic Algorithm and this correlation was compared with a correlation obtained using Quasi-Newton method. This comparing leads to one conclusion that using Genetic Algorithm is better than using of empirical correlations by means of results of statistical analysis done her. This work identified Reynolds number, gas to liquid densities ratio, gas to liquid viscosities ratio, volumetric solid concentration and Capillary number as expressive dimensionless groups to predicate the gas holdup in slurry bubble columns. Hence the developed Genetic Algorithm correlation should be useful in the scale up of slurry bubble columns. References • Albijanic B.C, Duric M, Ptrovic L. D, and Tekic M. "Prediction of gas holdup for Alcohol solutions in a draft tube bubble column", APTEFF, 2006, 37, 71-82. • Behkish A., (2004), “Hydrodynamic and mass transfer parameters in large-scale slurry bubble column reactor “, PhD thesis, University of Pittsburgh. • De Swart J.W., Van Vliet R.E., and Krishna R. " Size, structure and dynamics of large bubbles in two dimensional slurry bubble column", Chem. Eng. Sci., 1996, 51, 20, 4619-4629. • Hikita, H, Asal S., Tanigawa K., Segawa K., and Kitao M., "Gas holdup in bubble column" Chem. Eng. Journal, 1980, 20, 59-67, cited from (Albijanic 2006). • Koop K., Vendu C.O., and Krishna R. "Large bubble sizes and velocities in a bubble column slurry reactor", Chem. Eng, Technol., 2004, 27, No. 11, 1195-1199. • Melanie M, "An introduction to Genetic Algorithm s", A Brad Ford Books, 1998. Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤٢٠ • Mouza A.A., Dalakoglou G.K, and Paras. S.V. (2005) “Effect of liquid properties on the performance of bubble column reactors with fine pore spargers” Chem. Eng. Sci., 60, 1465 – 1475. • Ruthiya, K. C. (2005) “Mass Transfer and Hydrodynamics in Catalytic Slurry Reactors” PhD thesis, Technische University of Eindhoven. • Ruzick M.C., Drahos J., Mena P.C. and Teixeira J.A. " Effect of viscosity on homogenous –heterogeneousflow regime transition in bubble columns", Chem. Eng. Journal, 2003, 96, 15-22. • Shah Y. T., Godbole "Gas –liquid –solid reactor design ", Mc-Grow Hill, New York, 1979. • Shaikh A., Al-Dahhan M. (2003) “Development of an artificial neural network correlation for prediction of overall gas holdup in bubble column reactors” Chem. Eng. and Processing, 42, 599-/610. • Shirsat S., Mndal A., Kundu G., and Mukherjee D. "Hydrodynamic studies on gas liquid down flow bubble column with Non Newtonian liquids", IE(I) journal, 2003, 37, 39-43. • Vandu C. O. and Krishna R. (2003) “Gas hold up and volumetric mass transfer coefficient in a slurry bubble column “ Chem. Eng. Techno., 26, No. 7, 779-782. • Zou R., Jiang X., Li B, Zu Y. and Zhang L. "Studies on gas holdup in bubble column operated at elevated temperature", Ind. Eng.& Chem. Res., 27, 1988, 1910-1916, cited from (Albijanic 2006). Table (1) Data sources of experimental points No. Reference System No. of Exp. 1 Koop et.al. (2004) Air/paraffin oil/Alumina catalyst 43 2 Vendu and Krishna (2003) Air/Ethanol/Raney cobalt catalyst 26 Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤٢١ Table (2) Maximum and minimum for dimensionless groups. Variable Reynolds No. Density Ratio Viscosity Ratio Volumetric Solid Concentration Capillary No. Gas holdup Maximum 2.485 0.002 0.013 0.25 3469.56 0.229 Minimum 0.016 0.0016 0.002 0.01 25.03 0.014 Mean 0.8293 0.0017 0.0061 0.0996 640.8 0.1025 Table (3) Model summary of genetic algorithm. Profile Train error Input Hidden (1) Hidden (2) Output 5:5-6-1:1 0.02965 5 6 0 1 Table (4) The result of using QN method. Parameter a b c d e z Estimated -6.09 0.0837 -0.168 0.189 -0.0189 -0.015 Table (5) Comparing between SNN & QN methods. Correlations AARE % R SNN 10.8 0.988 QN 16.1 0.977 Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤٢٢ Figure (1), Genetic Algorithm block diagram Figure (2), Dialog box used in SNN. Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤٢٣ Gas Holdup Exp. 0.00 0.05 0.10 0.15 0.20 0.25 G a s H o ld u p P re d . 0.00 0.05 0.10 0.15 0.20 0.25 Figure (3), Experimental gas holdup verses predicated gas holdup using SNN. Gas Holdup Exp. 0.00 0.05 0.10 0.15 0.20 0.25 G a s H o ld u p P re d . 0.00 0.05 0.10 0.15 0.20 0.25 Figure (4), Experimental gas holdup verses predicated gas holdup using QN Al-Qadisiya Journal For Engineering Sciences Vol. 2 No. ٢ Year 2009 ٤٢٤ Gas Holdup Exp. 0.00 0.05 0.10 0.15 0.20 0.25 G a s H o ld u p P re d . 0.00 0.05 0.10 0.15 0.20 0.25 Gas Holdup (exp.) vs Gas holdup (pred.)SNN Gas Holdup (exp.) vs Gas holdup (Pred.) Q.N Plot 1 Regr Figure (5), Experimental gas holdup verses predicated gas holdup using SNN & QN.